What's this wire to? Everything seems to be working fine.

Looks like an in line fuse. One side coming from the battery, and the other going out to the load. Pop that cap off and you'll probably find a fuse in that housing. l'd recommend trying to get that wire reconnected properly if you can. Аlso, coming from the power source, that fuse won't be protecting anything. So if the exposed part grounds out on anything, it can do some real damage to your electrical system.