Moshe was a hundred and twenty years old when he died: his eye was not darkened, nor his moisture ceased. (Devarim 34:7)
Rashi and Ibn Ezra understand "moisture" as referring to the youthful appearance of the skin: Moshe's skin did not become dry and wrinkled as generally happens with old people.
The darkening of the eye, which also did not happen to Moshe, might seem to refer to blindness. This is slightly difficult because if so, you might expect the verse to refer to Moshe's eyes, not to a single eye. That does not seem like an insurmountable difficulty, but in any case I want to propose a different understanding of the word "eye", or rather, the Hebrew word "ayin" which is used here.
In some other places, we see that "ayin" means not "eye", but "appearance". (For example, here. And of course the concepts of "eye" and "appearance" are related so it makes sense that they would share a word.) Perhaps the same is true in our verse: it was not Moshe's eye that did not darken, but rather his appearance that did not darken (or become worse).
[I wanted to say that the same was true of Leah - that not Leah's eyes but her appearance was "weak", making the contrast between her and Rachel crystal-clear. But Leah's eyes are mentioned in the plural, so the meaning of "ayin" there is probably not "appearance". It was in the process of researching this possibility that I found the idea for my last post.]
If "ayin" in fact means "appearance" here, the descriptions of Moshe's "ayin" and "moisture" would be referring to exactly the same thing: the youthful quality of his skin. You can see such redundancy as a problem, or else as an advantage, because literary parts of Tanach often use parallelism. I'm undecided which possibility is more likely, and undecided whether blindness or bad skin is a likelier explanation overall.
As for why Moshe's face would have special healthy qualities even at age 120, I think it's impossible to avoid mentioning Shemot 34, where Moshe comes down from Mt. Sinai and his face is shining with some kind of special light, and as a result he has to put a mask over his face. It's not clear how long this shining lasted (it could be for the rest of his life, but I'm not convinced that's necessarily the case) but in any case, I think this shining quality is somehow linked to the special appearance Moshe's face had at the time of his death.