I believe it starts when you defeat level 50, a P in a blue square appears in the upper right section of the combat area and need to click on it 5 times to prestige. It resets you back to level 1 and gives an XP & Gold bonus to your next run, the minimum level you need to defeat goes up to be able to prestige again. If you wait and defeat more levels, the bonus you get will also increase. Not sure of exact scaling rate, but the next prestige will become available roughly 5 levels (based on highest level defeated).
So the longer you wait until you prestige, the better your bonus will be, but the higher you will need to go before you can prestige again. I am currently prestiging around combat level 275, I have only prestiged about 10 times total, my XP & Gold bonus is around x63.