The powerful Isu artifact repeatedly sought by Assassins and Templars in Assassin’s Creed is the Apple of Eden.
An Apple of Eden is a Piece of Eden, a group of advanced artifacts created by the Isu, the technologically sophisticated civilization that existed before recorded human history in the series’ mythology. Apples can influence human perception and behavior, making them valuable to factions seeking control.
The first Assassin’s Creed game centers on Altaïr’s discovery that the conflict between the Assassins and Templars is tied to Pieces of Eden. The artifact’s importance continues throughout the franchise, although different games feature different Pieces of Eden and different historical owners.
The Apple is not the only artifact in the series. Other Pieces include the Staff of Eden, the Sword of Eden, and the Shroud of Eden. The Animus is also unrelated: it is a modern machine used to access genetic memories, not an Isu artifact.