I just spent 1,000 exp points on level and nothing happened. So I was wondering what are exp used for? and what do they do?

It should have increased your level by one. It always works when I use exp so I'm not sure what you expected to happen or just didn't notice the change.

Your pet should have gained 1 level.

i.e., if your pet was level 27, it would have become level 28.

The other stats of your pet can be raised with exp as well.

Lol yeah I just didn't notice the change, its because I thought it was going to increase the level stats by 5 or something like that but I was wrong.

Just to let you know, the Exp cost for increasing level/stat never changes. I'd recommend hanging onto all you Exp until you're at a high enough level that it costs a lot of sp to train. ;)