The Garrison system includes NPC followers who can go on missions for you while you're offline for various benefits as well. This ends up nearly being a complete minigame - my first impression is that you can almost play an entirely new RTS minigame while playing WoW.
The Garrison feature seems like a massive hybrid combination of pet battles and the farm system, with NPC followers that you can send on missions, which level up, get geared up (yes, the even have gear) and the missions you can run depend in part on the structures you've erected in your garrison. The minigame of getting the right followers to play the missions you want, getting the right structures to unlock special missions is all part of the minigame.
You can also use the garrison purely as player housing - you can decide in what zone to place it, you can move it, and you can mount trophies in the town square. In short, instead of a player house, you get a player fortress.
Here's an example of a mock-up for the follower interface.
All in all it's a very detailed new feature. Buildings you choose to build can give you access to professions you don't normally have, missions you want to run, and even resource nodes like mines can be placed. All in all this looks to be a huge change and expansive feature to the game.