Power-leveling is a term mostly found in MMORPGs. Such games usually have a path which the devs intend for the players to level up: doing certain quests or missions, fighting certain foes at certain levels, using certain equipment, and so on.
Power-levelers take the short-cut to the top levels. There are several ways this can be done, depending on the game:
- Playing with other players at a much higher level than them. While they may not be effective in the fight in any way, the higher levels will earn xp much faster than the power-levelers could. This usually comes in the form of leeching.
- Doing whatever it is that gets the most xp per minute, no matter how repetitive. For example, the first warrior to reach level 40 from level 10 in Maple Story did it in 3 days(or so) by not doing a single quest or party-quest. They simply killed as many mobs as possible at the highest rate possible, only changing zones when they outleveled the last. While the player hit 40 much faster than any other players.
- Exploiting. For example, if a certain mob gives much higher rewards than they should, kill only them. This may result in punishments on the player when the exploit is caught.
- Using equipment much better than they are expected to. This generally involves being given the equipment by a member of a group, or the player giving it to themselves from a higher-level alt. This is generally too mild (and too common) to be considered power-leveling, but it may be the case if the equipment is considerably more powerful than the game is balanced for at that level.
While it can be debated that players have the right to play their games however they want, being called a power-leveler is often an insult. This is normally because there's a certain learning curve associated with these games, and skipping ahead of the curve may mean not having any idea how to play at their newly gained level. For example, in winter 2008, there was massive spawning of the giant snowman. Many people could level-up from level 10 to level 13(or so).
However, once players have already reached a high level on their own, it is generally considered somewhat more acceptable for them to power-level new alts.