I thought it was "rested XP" or am I thinking of another game? I never quite figured out what rested xp was exactly.
Rested XP doesn't exist in MH anymore.
How it used to work (and how it works in other games) is that you accumulate a pool of bonus XP based on the time you are logged out of the game. So, just using arbitrary numbers, if you were logged out for 24 hours when you came back you'd have a pool of 500,000 Rested XP. Any XP you earned while you had Rested XP would be doubled, and the bonus portion of that would get subtracted from your pool until it was empty.