Experience Points
Experience Points, usually abbreviated as EXP, are a recurring feature of the Dragon Quest series. Experience Points have been present in every main series game and nearly all spinoff games.
Experience Points are gained at the end of a random encounter or other battle as a reward. More powerful monsters reward greater amounts of Experience Points.
Level up
When a character accrues a specific, predetermined number of Experience Points, they will "level up" (that is, gain a level of experience) and receive statistical increases particular to their overall character type. In most games this is a characters of the party member, though in Dragon Quest III and Dragon Quest IX stat growth is dependent on the character's class.