apparently pet battles also grant AP (found one pet battle world quest right now that grant 100 AP).
World quesst work following way:
You open your map and it filled with different activities: pvp quests, profession quests(only available if you have 300+ profession), dungeon quests, apexis like quests, world boss quests, etc.
Every quest shows which reward it gives (right now there is 7 type of rewards: Gold, AP, Battle pet charms(only for battle pet quests), Blood of sargeras (top tier crafting resource), items (they scale based on your current ilvl up to mythic dungeon quality if i am not mistaken) and common resources, order hall resources
All those quests are attached to one of the faction. Each day you recieve task to comlete 4 world quests for one of the factions, After completing 4 quests you recieve a chest that contains additional random reward (and reputation with that faction of course).
Here the screenshot for example:
http://screencast.com/t/szrqdvjR