Have you ever wondered what it would be like to have Leeroy Jenkins, Milhouse Manastorm or Archmage Vargoth as your companions and friends? Well, wonder no more! It's like pet battles, only with NPC's! You can collect as many followers as you like for your garrison, but there's a limit on how many you can have active at a time - think of it as a 'too many cooks' situation. Each follower has specific abilities that make them better or worse for specific missions (some have crowd control, for example) and some followers will even be your bodyguard, accompanying you on missions and protecting you as you (and they) level up.
For more details, please check out this third preview of the Garrison feature coming in Warlords of Draenor.