Training
Training is one of the ways to improve your character, and is the main method of learning new abilities. It will not generate as much experience as going on quests or fighting, but there is the possibility of getting stat points as well.
You can train anywhere if you really want to. No one is stopping you. But training on your own will only get you so far. You can't learn any abilities by training wherever, and stat points are difficult to get. However, if you go to a school, you can not only learn whatever abilities the instructor has to offer, but you can gain multiple stat points a session.
Training is mostly for increasing your character's options, rather than your character's power.