Faction

Faction likely refers to:
 * Balthazar faction, reward points awarded for PvP accomplishments.
 * Imperial faction, a measure of how much you have accomplished for the Imperials
 * Kurzick faction, a measure of how much you have accomplished for the Kurzicks
 * Luxon faction, a measure of how much you have accomplished for the Luxons

Factions almost always refers to
 * Guild Wars Factions, the second campaign

Trivia

 * Initially, the PvP reward system awarded faction (without any adjective); these were renamed as Balthazar faction to distinguish them from Kurzick/Luxon-specific points.