The character you play Altair (الطائر, Arabic, "The Flying One"), a member of the Hashshashin cult, is tasked with killing nine prominent people who are propagating the crusade.
The story takes place in Acre, Jerusalem, Damascus and Masyaf. Each city is accurately depicted and true to the period the game is set in. Also all the people that Altair assassinates are historical figures who either died or disappeared in 1191, though not necessarily through assassination.
The game itself is outstanding, and the producers should be highly praised for the inventiveness shown in this game. The way Altair interacts with the environment and the slowly unfolding conspiracy all point to the amount of work the programmers have put into this product. I cannot recommend this highly enough.
And if you are looking for more information on the Hashshashin cult try reading The Assassins. A radical sect in Islam by Bernard Lewis.