Most of Assassin's Creed (2007) is set in 1191.
The game takes place during the Third Crusade, a period of conflict involving Christian and Muslim forces in the Holy Land. Its principal locations are the cities of Jerusalem, Acre, and Damascus, while the protagonist Altaïr Ibn-La'Ahad carries out missions across the region.
The year is significant because it places the fictional Assassin Brotherhood within a recognizable historical setting. The game combines real figures and events with its own science-fiction mythology, so it should not be treated as a literal retelling of the Crusades. Altaïr's targets and many political details are dramatized for the story.
A common mix-up is confusing the game's historical setting with the modern-day sections involving Desmond Miles. Those scenes occur in the contemporary period, while 1191 refers to the principal historical narrative experienced through the Animus.