Players can earn Faction Points by completing tasks for and killing the enemies of any faction in the game. This applies in space and on the ground. However, when most players mention faction points (commonly abbreviated "FP"), they are referring to faction standing with either of the Galactic Civil War factions, the Rebel Alliance or the Galactic Empire.
Faction points can range from -5,000 to 5,000.
Being killed by a player of the opposite GCW faction will cost the victim some points of their own faction.
See Faction Rank for description of GCW Points.