Experience is what makes the world go 'round. Well, experience and money, but money will not level your character (directly).
Well, it could level your character directly, but that is Evil™.
In many games, mobs that are closer to your own level offer the best XP per kill. For example, in City of Steam, a level 27 player attacking level 31 Brood in Dimpoint will get 20 XP per kill, but in Ebonwax, fighting level 30 Brood, he gets 30 XP per kill. Although you may be able to kill something 6 levels above you, you will get so little XP at that point (about 1 XP per kill) that it is pointless.
Some games have some game-specific notes about Experience and Leveling: