Civilians are non-combat units that show up on Terror Site missions. As in the original games, the goal of the mission is to save as many civilians as possible.
Civilians will cower behind cover, although they derive no benefit from it. They will sometimes run away from aliens on their turn. Your units can "rescue" civilians by moving a soldier adjacent to them. The civilian will immediately be removed from the battlefield and considered "saved". It is not necessary to do this in order to win the mission, as any civilians who survive will count. However, a rescued civilian is one less potential Chryssalid, greater freedom to use explosives and fewer pieces of cover tied up by useless targets.
Civilians do not exist on any other map type - Abduction missions begin with all civilians already wrapped up in green stuff, ready for experimentation, while the extra units on Extraction and Escort Council missions are a distinct unit type.