Many Role-Playing Games, and most Roguelikes employ experience points and experience levels as the core character advancement method.
A character will usually gain experience by killing monsters. Other methods include defeating traps, identifying items by trying them out, casting a spell for the first time, fulfilling quests or other sorts of tasks.
When a certain amount of experience is gained, the character advances one level. Some games have magic spells, skills, or stat points associated with levels, so that a character may learn a new spell or skill, or become stronger or smarter upon "leveling up".
Most games make each level increasingly difficult to attain. This is called the experience curve.
The experience levels define how experienced a character is at surviving inside the game world; they are usually related to the strength and overall performance of the character.