To Quest or Grind

There is only the one way to level in World of Warcraft and that is to gain more experience. Experience can be gained in two ways. From completing quests or by killing monsters of high enough level to give experience.

The only monsters that will give experience are those that are within a few levels below your current level and up. Attacking mobs 3 or 4 levels above you will probably be a quick trip to the local graveyard and a long run back to your corpse.

The repeated killing of experience level mobs is know as grinding. Boring? Yes, it is. Killing mobs 1 or 2 levels below you is the fastest experience. They give slightly less experience than monsters your level but the recovery time is less and they die faster

Completing quests is more interesting, although it can sometimes involve a bit amount of grinding when you are looking for rarer items. With quests you can complete errands for Non-Player Characters (NPCs). This may involve something as simple as running a message to another NPC but usually involves... well... killing mobs.

Whether you gain your experience, and thus progress to the next level, by questing or grinding really comes down to your own choice. Bored by killing? Go quest. Need a quick level for the battlefields? Go grind it out.

My personal choice is to quest whenever I can. I play Warcraft for pleasure, not to gain levels faster than anybody else.

Your choice may be different.