Most people give little thought to rested exp. It was added to help the more casual player 'keep up' with their more driven friends, and does that pretty well. but in the case of running alts its a goddess send.
here is what the community site has to say about resting, ill cover the basics here too.
When your in an inn or a city you get little 'zzz' over your character level in your portrait. Your now earning rested experience. A tiny bit when your online and a bit more when you log off in that area. You can gather enough exp through it to get you to half way through your next level. So if you were level 1 and logged out you could save enough bonus exp equal to the exp mid way from level 2 to level 3 (1.5 levels).
It only affects monster slaying exp, increasing it by 100%.
So why is it so great for running alts?
If every time you swap characters you make sure to log out in an inn or capital city you will be earning 'free' exp. If you bounce from character to character you can use that to speed up the groups leveling speed. At 3 or 4 characters in fact you can almost be certain to always have it up helping you along.