Factions are the different groups of cards available to play in the game. There are 5 factions in the game: Winter Pact, Swarm of the East, Ironclad Union, Tribes of Shadowfen, and Neutral. Each faction has two unit types, except for neutral, which has a variety of them. Each faction has its own unique abilities, documented here by BenQ.
For more information about each faction, see their pages here.