It is pretty easy for Christians to skip along reading “the eye is the lamp of the body” and not give one ounce of consideration to what is being said: How, we should be asking, can an eye be seen as a “lamp”? And, if an eye is good, how does that make the “body full of light”? And if an eye is bad, how can it be that the body is full of darkness? Therein lies an ancient physiological lesson.
Put simply, it is this: the eye is seen as a lamp that exudes light — or does not exude light. Some ancient actually thought lights gave forth light that permitted humans to see, and if the eye gave off light, it was because the inner being was full of light.
But Jesus’ point is not about the extramission theory of light; it is a lesson on morality. What does it mean to have a “good” or a “bad” eye? Again, the answer is that it refers to generosity or stinginess. Here is a reference: Prov 22:9 (‘the good-eyed man’ is kind to the poor). And Jesus drives the point home: if a person is full of darkness, how deep is that darkness!
Unpacked, Jesus is here talking about the necessity of a heart being transformed by God’s grace, or at least a heart being good for if the heart is not good, nothing can be good. And the direction of this transformation, in these verses, is all about generosity.
There is a correlation, not simply as a one-to-one but still a correlation, between what one does and what one is: good deeds reflect good hearts. Here is a good rabbinic saying, from J. Neusner’s translation of the Mishnah, Avot 5.19:

A. Anyone in whom are these three traits is one of the disciples of Abraham, our father;
B. but [if he bears] three other traits, he is one of the disciples of Balaam, the wicked:
C. (1) a generous spirit, (2) a modest mien, and (3) a humble soul—his is one of the disciples of Abraham, our father.
D. (1) a grudging spirit, (2) an arrogant mien, and (3) a proud soul—his is one of the disciples of Balaam, the wicked.
E. What is the difference between the disciples of Abraham our father and the disciples of Balaam the wicked?
F. The disciples of Abraham our father enjoy the benefit [of their learning] in this world and yet inherit the world to come, as it is said, That I may cause those who love me to inherit substance, and so that I may fill their treasures (Prov. 8:21).
G. The disciples of Balaam the wicked inherit Gehenna and go down to the Pit of Destruction, as it is said, But you, O God, shall bring them down into the pit of destruction; bloodthirsty and deceitful shall not live out half their days (Ps. 55:24).