A faction is a group of allies, either racial or ideological. Most in-game factions are described in Warcraft lore, but some were specifically introduced in World of Warcraft.
The concept of a faction exists primarily in World of Warcraft. The use of factions in other Warcraft games is more for general grouping purposes and not quantitatively tracked like World of Warcraft.
Most factions are tracked in World of Warcraft by the reputation that a player character has with each faction. Some groups that are not tracked as factions appear in the organization list.