You start with 7 keys by default and you get them back after a Time Loop. You need keys in order to open up chests that you receive from boss battles. These chests hold items or various goodies inside and it's usually a good idea to open them as soon as you have the chance. Some players believe, though, that opening chests reaps better rewards if you do so in the later stages, but I'm not really sure about that. The only thing that's clear to me is that the rarer the chest, the better the rewards. But try to micromanage your keys in such a way that you will always use them all to open chests before a Time Loop.