You earn experience by defeating monsters and completing quests. Leveling up results in increased health, mana, and stats. You will see a special level up message when you reach the required experience.
Leveling up earns you 1 ability point. Ability points can be allocated towards ability enhancements to strengthen them. You can learn more about ability points here.
You will unlock a new ability every 5 levels (1, 5, 10, 15, etc...)