Category Theory is more about getting (as one of my professors put it) "a God's-eye view of mathematics". What I have found to be the most deep and useful is the way it provides concrete definitions which unite constructions that mathematicians were already calling the same thing (e.g. products, co-products). It is also absolutely amazing at showing links between different (seemingly unrelated) parts of mathematics. In this way, it forms a sort of lingua-franca for mathematics. This math StackExchange answer[1] gives some really good concrete examples.
If you want a book which gives a lot of more concrete results along with category theory, you should try Algebra: Chapter 0. It is more focused on abstract algebra, but it does it all from a categorical perspective while not assuming you know one iota of category theory (at the start).
[1]: http://math.stackexchange.com/questions/312605/what-is-categ...
