Experience points are a common method of measuring a character's increasing skill and power of the course of a game. Experience points, commonly abbreviated as XP, are earned by characters as they overcome challenges in the course of their adventures. This most obviously includes combat encounters, but also includes social intrigues, stealthy infiltrations, and other situations where a favorable outcome is not assured.
This abbreviation is where the version of Microsoft Windows got it's name.
Experience points reflect a character's advancement in two main ways, depending on the game. These are not exhaustive, but they cover the majority of games.
In the first style, a character accumulates experience until he reaches a preset threshold. Reaching this threshold signals an increase in power. Usually, this manifests as the character gaining a level in an appropriate class. A single experience point in this style of advancement is relatively small. Characters may need thousands of experience points to reach the next level, but a character may be rewarded with hundreds or thousands of experience points per game session. As examples, this type of advancement is found in Dungeons & Dragons and Decipher's Star Trek RPG.
The second style uses experience points as a kind of currency used to purchase increases in a character's abilities. This allows a smoother increase in power compared to level systems and often allows a player to have greater control over her character's advancement, but it is often more difficult to gauge the relative power of a character at a glance. A single experience point is typically more precious in these games; a character will usually earn fewer than ten per session. Vampire: The Masquerade and Silhouette games such as Jovain Chronicles use this kind of experience points.
For comparison, Call of Cthulhu is a game which does not use experience points in the usual sense.