Symbolism, Imagery, Allegory
We know you might be tired of hearing all about the Greeks and how they invented tragedy, but bear with us: it's going to pay off.
The most famous Greek tragedy today would definitely be Sophocles' Oedipus Rex. Oedipus, among lots of other problems, unforgettably ends this play by blinding himself, largely out of disgust with himself and his inability to see the truth.
So, blindness, tragedy, and self-knowledge are all interconnected images that have a history almost as old as tragedy itself. Like Samson, Oedipus feels responsible for his tragic circumstances and, like Samson too, he feels powerless to do anything about it. For both Oedipus and Samson, then, their blindness is a physical reflection of an internal failure: they both failed to see—metaphorically—the truth about someone or something in their life.
Blindness and knowledge have a further connection in Greek literature (we told you!) in the character of Tiresias, a famously blind prophet who pops up in various myths, tragedies, and epics. He's a prophet with a particular talent at telling the future. The idea is that, because he can't see the world in front of him, he has a special ability to see the true nature of things.
This is a super common literary trope. Homer, the alleged and possibly fictional poet of The Odyssey and The Iliad, was supposed to be blind. And it's no wonder that Milton liked it: he, too, was a blind seer.
Milton takes this Classical and pagan attitude toward blindness and sets it in a Christian universe. Ever since those famous Biblical words of creation in Genesis—"Let there be light!"—the Judeo-Christian God has been associated with light while Satan, evil, and chaos in general have been associated with darkness. So you can't really blame Samson for feeling that by having light taken from him, he's somehow lost touch with God.
You could even argue that the most important thing that happens in the poem is that Samson learns how wrong he is. In fact, there's an important difference between the kind of knowledge you gain from physically looking at the world, which doesn't seem to have done much for Samson, and the kind you gain from looking into yourself.
It's the second kind that actually makes Samson act: "I begin to feel/ Some rouzing motions in me which dispose/ To something extraordinary my thoughts" (1382-4). His blindness becomes a kind of interior sight or vision—more accurate than exterior sight, and ultimately more important.