See is what your eyes do. However, this word has loads of meanings: you can see a shrink, which means you're consulting a psychiatrist; or you can be seeing your high school sweetheart, which means you're dating him.
See usually means passively observing, while look, which is also something you do with your eyes, is more active and intentional. When someone says, "The president will see you now," the president is sitting there passively, waiting for you to be shown in. You can say "I see," to mean "I understand; I get it." Or you can look into your crystal ball and see into the future, in which case you'd be called a seer.