The Rest Bonus is a feature that is there for those people who cannot play all the time. For every second that you are offline, a Rest Bonus Pool will increase in size by 20 EXP Points. Once you login again and kill a monster, for as long as your Bonus Pool is filled, you will get double experience points from that monster. The maximum amount of exp you can save up is about 1 week's worth.
You log off in Prontera.
You log off for 3 hours. (3 Hours = 180 Minutes = 10,800 Seconds) According to the Resting System, you get 20 Exp every second that they are offline.
That means 10,800 Seconds * 20 Exp per Second = 216,000 Exp accumulated total.
You log in at the end of the 3 hours and kill something that gives 15,000 Exp. The exp will be doubled by depleting from the Rest Buffer.
You will then gain 30,000 Exp for the kill and your Rest Buffer will decrease by 15,000 Exp leaving you with 216,000 - 15,000 = 201,000 Exp.
You will continue to get the Rest Bonus until your Buffer is empty.
Note: Your Rest Buffer will only fill up for 7 days. If you log off for longer than seven days, your Rest Buffer will not continue accumulating beyond seven days (604,800 Seconds). That means your Rest Buffer can only accumulate 12,096,000 Exp maximum.