Poor in Spirit
What does it mean to be poor in spirit? In the parallel passage in Luke, the word spirit is left out. Here Matthew uses it to distinguish the poor in spirit from those who are poor materially. To be poor in spirit is to realize your spiritual poverty. You are a beggar looking for scrapes of food. (The Greek word rendered poor usually referred to a beggar.) If you were rich, you would not need the help of another. But being poor you know that you can’t get anywhere without someone else’s help:

Luke 18:13 But the tax collector, standing far off, would not even lift up his eyes to heaven, but beat his breast, saying, ‘God, be merciful to me, a sinner!’

The kingdom of heaven belongs to those who realize their poverty. They know that they lack the means to do anything that will make them worthy of the kingdom. They come to God empty handed. Realizing that we are poor in spirit is the first step in our Christian walk.
Mourners
Once you understand your spiritual poverty you mourn. You are not worthy to be a child of God. You are not doing what the creature was created for: to glorify God. We understand the depth of our rebellion and that causes us deep distress:

Psalm 51:4
Against you, you only, have I sinned
and done what is evil in your sight,
so that you may be justified in your words
and blameless in your judgment.

We not only mourn over our sin but the consequences of our sin.
But our mourning also takes on another aspect. Our love for God causes us to mourn not only our sin but the sins of others. It grieves us when the God that we love is being dishonored:

Psalm 119:136
My eyes shed streams of tears,
because people do not keep your law

The Greek word rendered mourn “indicated a sorrow that begins in the heart, takes possession of the entire person, and is outwardly manifested.” (Hendriksen, pg. 271)
Those who mourn will be comforted. Our sorrow turns us to God and God forgives us of our sins. He gives strength and reassurance.

Psalm 30:5
For his anger is but for a moment,
and his favor is for a lifetime.
Weeping may tarry for the night,
but joy comes with the morning.

Psalm 50:15
and call upon me in the day of trouble;
I will deliver you, and you shall glorify me.
Isaiah 55:6-7
“Seek the Lord while he may be found;
call upon him while he is near; [7]
let the wicked forsake his way,
and the unrighteous man his thoughts;
let him return to the Lord, that he may have compassion on him,
and to our God, for he will abundantly pardon.

We are also comforted with the knowledge that our God reigns and one day all will submit to His Lordship.
Sometimes the comfort comes in the affliction being removed, sometimes the comfort is that the affliction lasts but is alleviated by the knowledge that it is nothing compared to the glory that will be revealed when Christ returns:

Romans 8:18-23 For I consider that the sufferings of this present time are not worth comparing with the glory that is to be revealed to us. [19] For the creation waits with eager longing for the revealing of the sons of God. [20] For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope [21] that the creation itself will be set free from its bondage to decay and obtain the freedom of the glory of the children of God. [22] For we know that the whole creation has been groaning together in the pains of childbirth until now. [23] And not only the creation, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for adoption as sons, the redemption of our bodies.

The Meek
What is the difference between meek and poor in spirit. Being poor in spirit is something that is personal, it is how we view ourselves — it is the realization of who we are. Meek is in relationship to God and man, it is a character trait.
From Psalm 37 we see that the meek person waits on the Lord, he does not take revenge on evildoers but trusts in the Lord and waits upon Him. His confidence is in the Lord and he leans on Him. He takes refuge in the Lord and does not lean on his own righteousness but on the righteousness of the Lord. But meekness is not weakness, the meek are strong not doormats.
After realizing our poverty and mourning our rebellion against God, we meekly submit to the statutes of the Lord. We meekly follow Him and submit to His kingship.
The meek shall inherit the earth. The promise in the Old Testament was that the meek would inherit the land:

Psalm 37:11
But the meek shall inherit the land
and delight themselves in abundant peace.
Psalm 37:22
for those blessed by the Lord shall inherit the land,
but those cursed by him shall be cut off.
Psalm 37:29
The righteous shall inherit the land
and dwell upon it forever.
Psalm 37:34
Wait for the Lord and keep his way,
and he will exalt you to inherit the land;
you will look on when the wicked are cut off.

The inheritance of the people of Israel was the land of Israel. If the nation continued in following the statues of God and putting their trust in Him, then they would continue in the land. So, in the Psalms we see that the blessedness that comes from being meek, is the actually inheritance of the land.
Our inheritance is the whole earth, not just Israel:

Romans 4:13 For the promise to Abraham and his offspring that he would be heir of the world did not come through the law but through the righteousness of faith.

Those Who Hunger and Thirst for Righteousness
After realizing our poverty, mourning our rebellion and meekly submitting to the Lord, we crave righteousness. Each of us knows that we have fallen short of the glory of God:

Isaiah 64:6 But we are all as an unclean thing, and all our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities, like the wind, have taken us away.

God, in His mercy, has given us a way to be reconciled to Him, even though we are unclean and He is holy. We have been given Christ’s righteousness, it has been imputed to us (meaning it has been transferred to us):
Even though we are now consider righteous by God, we are righteous by faith and not by sight. We can’t see this righteousness and we don’t experience it in our lives because it is alien to us, it is outside of us. Luther says that we are a snow covered dung heap. We don’t become righteous, but we long for it. We know that we should be different because we have died to sin. We long to experience by sight what we know be faith we possess.
We thirst and hunger for it the way the deer pants for water:

Psalm 42:1b
As a deer pants for flowing streams,
so pants my soul for you, O God.

And those who pant for God and His righteousness will be filled and we will be satisfied:

John 4:13-14 Jesus said to her, “Everyone who drinks of this water will be thirsty again, [14] but whoever drinks of the water that I will give him will never be thirsty forever. The water that I will give him will become in him a spring of water welling up to eternal life.”
Isaiah 49:9-10
saying to the prisoners, ‘Come out,’
to those who are in darkness, ‘Appear.’
They shall feed along the ways;
on all bare heights shall be their pasture; [10]
they shall not hunger or thirst,
neither scorching wind nor sun shall strike them,
for he who has pity on them will lead them,
and by springs of water will guide them.
Isaiah 55:1
Come, everyone who thirsts, come to the waters;
and he who has no money,
come, buy and eat!
Come, buy wine and milk
without money and without price.
John 7:37-38 On the last day of the feast, the great day, Jesus stood up and cried out, “If anyone thirsts, let him come to me and drink. [38] Whoever believes in me, as the Scripture has said, ‘Out of his heart will flow rivers of living water.’ “

Who receives these streams of water? Those who believe in God, the citizens of the kingdom.
The Merciful
The Scriptures are very clear, since we have been shown mercy, in gratitude we should show mercy to others:

Matthew 18:33 And should not you have had mercy on your fellow servant, as I had mercy on you?’
Romans 15:7 Therefore welcome one another as Christ has welcomed you, for the glory of God.

God’s mercy comes first and out of that flows our mercy. And even though we show mercy to others, and we grow in our knowledge of God, we still continue to sin and so still need the continuation of God’s mercy. God’s mercy will be given to those who show mercy to others:

Matthew 6:14-15 For if you forgive others their trespasses, your heavenly Father will also forgive you, [15] but if you do not forgive others their trespasses, neither will your Father forgive your trespasses.
James 2:12-13 So speak and so act as those who are to be judged under the law of liberty. [13] For judgment is without mercy to one who has shown no mercy. Mercy triumphs over judgment.
2 Samuel 22:25-26
And the Lord has rewarded me according to my righteousness,
according to my cleanness in his sight. [26]
With the merciful you show yourself merciful;
with the blameless man you show yourself blameless;

But we have to keep in mind that this is not owed to us by God and that we are only merciful because God was merciful to us and we have to also keep in mind that God is merciful to those who do not show mercy. He was merciful to me when I was yet dead in my sins:

Romans 9:15-16 For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” [16] So then it depends not on human will or exertion, but on God, who has mercy.

The Pure in Heart
The blessedness of the pure in heart is reflected in the Old Testament:

Psalm 24:3-5
Who shall ascend the hill of the Lord?
And who shall stand in his holy place? [4]
He who has clean hands and a pure heart,
who does not lift up his soul to what is false
and does not swear deceitfully. [5]
He will receive blessing from the Lord
and righteousness from the God of his salvation.
Psalm 73:1
Truly God is good to Israel,
to those who are pure in heart.

But we have a problem, none of us is pure:

Romans 3:10-12 as it is written:
“None is righteous, no, not one; [11]
no one understands;
no one seeks for God. [12]
All have turned aside; together they have become worthless;
no one does good,
not even one.”

Moses wanted to see God but could not:

Exodus 33:18-20 Moses said, “Please show me your glory.” [19] And he said, “I will make all my goodness pass before you and will proclaim before you my name ‘The Lord.’ And I will be gracious to whom I will be gracious, and will show mercy on whom I will show mercy. [20] But,” he said, “you cannot see my face, for man shall not see me and live.”

It is only those who have had their hearts purified by the Lord who will be able to see God:

Psalm 51:10-12
Create in me a clean heart, O God,
and renew a right spirit within me. [11]
Cast me not away from your presence,
and take not your Holy Spirit from me. [12]
Restore to me the joy of your salvation,
and uphold me with a willing spirit.
John 17:24 Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world.

Now, we see God by faith, but there will come a time when we will actually see God. Moses was finally able to see God’s glory and we will be able to as well. This is a tremendous statement when you think about what has been said about access to God throughout the Old Testament.
The Peacemakers
All of humanity is born at war with God, we are all in need of reconciliation to Him:

Romans 3:17 and the way of peace they have not known.
Romans 5:10 For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life.
2 Corinthians 5:18 All this is from God, who through Christ reconciled us to himself and gave us the ministry of reconciliation

God did not create us to be at enmity with Him, we were created in fellowship but the fall broke that fellowship and the only way to reconcile God and man is through the God-man Jesus Christ:

Colossians 1:19-20 For in him all the fullness of God was pleased to dwell, [20] and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross.
Romans 5:1 Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ.
Ephesians 2:17 And he came and preached peace to you who were far off and peace to those who were near.

He brought peace to us and as His ambassadors we tell others of the peace He brings to them:

Matthew 10:11-14 And whatever town or village you enter, find out who is worthy in it and stay there until you depart. [12] As you enter the house, greet it. [13] And if the house is worthy, let your peace come upon it, but if it is not worthy, let your peace return to you. [14] And if anyone will not receive you or listen to your words, shake off the dust from your feet when you leave that house or town.
2 Corinthians 5:20 Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God.

And by doing this, others will know that we are sons of God.
Not only do we tell others of the peace that we have with God, we show them by our actions and love that we can have peace with each other. God not only reconciled us with Himself but with each other as well.
Being a people of peace is something that is important and is emphasized throughout Scripture:

Hebrews 12:14 Strive for peace with everyone, and for the holiness without which no one will see the Lord.
James 3:18 And a harvest of righteousness is sown in peace by those who make peace.
Colossians 3:15 And let the peace of Christ rule in your hearts, to which indeed you were called in one body. And be thankful.

Those Persecuted for Righteousness
And believe me it will bring persecution. When we stand up for the truth of God’s word, we will be despised for it. Even in the Christian community. People do not want to hear our message, they don’t want to change.
When a light is turned on in a dark room it hurts the eyes. Our righteous deeds and the word of God is like a blinding light in darkness. People want to turn away but can’t and so they try to turn out the light, to just get rid of it. If they could kill us, the way they did the prophets, they would.
This hatred between the people of the world and the people of God began after the fall:

Genesis 3:15
I will put enmity between you and the woman,
and between your offspring and her offspring;
he shall bruise your head,
and you shall bruise his heel.”

We see this enmity when Cain killed Abel and throughout the history of Israel in the Old Testament, the prophets spoke from God and yet the people ignored them and persecuted them.

Luke 13:34 O Jerusalem, Jerusalem, the city that kills the prophets and stones those who are sent to it! How often would I have gathered your children together as a hen gathers her brood under her wings, and you would not!
Matthew 23:29-31 “Woe to you, scribes and Pharisees, hypocrites! For you build the tombs of the prophets and decorate the monuments of the righteous, [30] saying, ‘If we had lived in the days of our fathers, we would not have taken part with them in shedding the blood of the prophets.’ [31] Thus you witness against yourselves that you are sons of those who murdered the prophets.

Acts 7:52 Which of the prophets did not your fathers persecute? And they killed those who announced beforehand the coming of the Righteous One, whom you have now betrayed and murdered

But our persecution does not compare to the glory that will be revealed on the last day, when we will receive the kingdom of heaven.

1 Peter 4:13 But rejoice insofar as you share Christ’s sufferings, that you may also rejoice and be glad when his glory is revealed.