To power level is a term used to describe when a low level character gets a higher level character to kill high level monsters to give the low level character experience to level up. This is often used in Prophecies, when a low level character will get a run to Droknar's Forge from Beacon's Perch to purchase max armor. Then, they will usually use scrolls (such as Scroll of Berserker's Insight and Scroll of Slayer's Insight) to increase experience gain and make the process quicker while a level 20 friend kills foes around Droknar's Forge. This quickly levels up the character without much effort and allows the character to progress quickly through the game without having to complete missions and such to reach level 20.
If you have Eye of the North, the fastest and most efficient way to power level yourself is by repeating the quest Kilroy Stonekin's Punch-Out Extravaganza!. This yields tons of experience, making it possible to get from level 10 to 20 in less than an hour.