One of the few things I always regretted after a couple of months of playing wow is that I didn't have the presence of mind to create 1 character of each class and simply only play them when I feel like it.
Rather than that I focussed on my lovely warlock which for the longest time was the only character I had thus forfeiting the wonderful benefits of rested xp.
Whenever you log out in an inn or in a capitol city (and to a lesser extend everywhere else) you start building up 'rested xp'. Rested xp builds up at around 1.5 levels every 6ish days or so and while you have rested xp you gain double xp for all kills you make. 1.5levels is also the maximum amount of rested xp you can build up so keep this in mind if you want to get the most out of your rested xp.
Since the gain in rested XP is constant and your levelling curve is not (it gets harder to get to the next level the higher your level is) the relative value of rested xp increases the higher you get in terms of levels.
So assume you're at a fairly low level and you need about 10000 xp to get to the next level. Since you're low level you'd be making about 50xp per kill (ignoring quests and such).
That comes down to about 200 kills or 100 kills with rested xp.
At much higher levels you'd need about 400k xp and you make about 500xp per kill.
That translates to 800 kills unrested and 400 kills with rested xp.
Now lets assume you need about 30 seconds to make a kill (may vary of course but it's easier on the math).
So at low levels your time benefit with rested xp is about 30x100 = 3000 seconds or 50 minutes
At high levels the effective time saved with rested xp translates to 30x400 = 12000 seconds or 200 minutes
This means being fully rested translates into an extreme timesaver at high character levels.
Especially if you only have limited time to spend a day and even if you are not overly interested in progressing as fast as possible it's a nice boon to take into account.
The nice thing here is that the effect is cumulative. The more characters you have the more potential you have to only be playing characters that have rested xp and thus the faster your characters overall progress.
Ideally you'd want to have a situation where you focus your play on 1 main character and then once in a while play the other characters rested xp. That way you'll have a nice and powerful main character but you're also getting the most out of your other characters.
You can make a nice rotation out of it if you don't mind switching characters or alternatively be like me and play another character when you feel like it knowing that all your other characters are building up rested xp.
I now have 1 character of each class and even though some of them suffer from neglect I can rest assured that the next time I play them their progress will be nice and fast (at least for the next 1.5 levels).