The rest state works as follows:
Across the bottom of your screen is an experience bar. At the point where you would gain 20,000 exp, a little notch appears in the bar. Until you cross that first notch, you are considered to be "well-rested" and gaining experience at what is in theory double the normal rate. You then become "rest" which is an extra 50%. 20,000 later you go to normal, then to tired (1/2 normal), and finally exhausted (1/4 normal). You can reset to well-rested by remaining within an inn for 8 consecutive hours.
Here's the catch: this experience only applies to mob-death experience. Exp you get from doing quests does not apply towards this, and if you finish a quest worth 3000 exp, the notch will slide that far as well.
Now, they are changing it to be scaled to level, but as of right now, 20000 exp is about the amount it takes to go from level 1 to 5 or 6. Or, it's about the amount it takes to go from level 30 to level 30.2. When the mobs are worth considerably more experience, you get tired much more quickly.
Ideally, you will get much of your exp from questing, and the rest from killing quest-related creatures. The whole system is tuned to be very anti-monster-slaying. Basically Blizzard doesn't want you sitting in one place killing the same creatures over and over again because they yield optimal exp. Not that the game isn't already tuned this way due to the quest system. Eventually, though, even while questing at level 30+, you will become exhausted while doing quests. It's inevitable since you can go from one end to the other and barely finish one level. The leveling curve is quicker than in, say, Everquest, so that's fairly significant. Notwithstanding that, you only get skill points from experience for killing creatures (every 300 before the rest modifier), so that gives people a reason to just kill creatures so they can advance their tradeskills.
I'm not really sure why I like the rest system. There are a lot of people who hate it horribly. They think it's stupid, they think it adds very little realism or RP to the game, they think there isn't a single real reason for it to be implemented. And they're right. I can never find one. It doesn't slow down power gamers, they just power quest instead. It really just slows down the people who play for 5-6 hours on the weekend rather than 1-2 hours every night, while making leveling more and more depressing as the day goes on.
Only the exceptions can be exceptional.