Think of a repository as a storehouse, a place where things are kept until needed. A silo is a repository for animal feed, and a trivia buff's mind is a repository for useless information.
The noun repository has a somewhat formal ring to it — why not just call a storehouse a storehouse, right? Think of a repository as somewhat more important and imposing than just a place to dump stuff. It has more of an air of authority, like the things stored there could change the world. Consider nuclear waste — would you rather store it in a dump or a repository? I don’t know about you, but I'd prefer the latter—sounds safer.