The levels game mechanic refers to games where you level up you character or anything that allows some sort of a level. The image above shows a player from World of Warcraft elevating to level 13. Leveling up can be done by earning the right amount of experience points which then lets you level up. By leveling up the character, the character can then wear different weapons and gear and also use stronger skills.
This is another definitive game mechanic that I would include in any game I would create if possible.