A faction is a group of allies, either Racial or ideological. Most in-game factions are described in 7th lore, but some were specifically introduced in 3rd. The concept of a faction exists primarily in all the Ages. The use of factions in other 7th games is more for general grouping purposes and not quantitatively tracked like 3rd Age.
Most factions are tracked in 3rd by the reputation that a player character has with each faction. Some groups that are not tracked as factions appear in the organization list.