You can learn professions at any level, you just need money to learn it.
You can learn up to two primary professions (Herbalism, Alchemy, Blacksmithing, Mining, Skinning, Leatherworking, etc etc). So generally, pick two that go together, skinning is the gathering profession for leatherworking, mining for blacksmithing, herbalism for alchemy.
The purpose is to give yourself something to do, really. It's fun to level it up and you can make some pretty awesome stuff.