Abbreviation of civilisation.
"The historical analysis focuses on how trade routes connected different civs across ancient Europe and Asia."
Abbreviation of civil.
"The official letter was marked as civ to indicate it pertained to a non-military matter rather than an emergency deployment."
Civilization, a turn-based strategy video game from 1991 (and various sequels) in which the player attempts to build and maintain an empire throughout history.
"After playing Civ for hours last night, I finally managed to conquer the entire world as Rome before sunrise."