The Apple of Eden is an artifact sought by both Assassins and Templars in Assassin's Creed.
The Apple is one of the Pieces of Eden, powerful artifacts created by the Isu, an advanced civilization that existed before recorded human history in the series' mythology. It can influence minds and produce other extraordinary effects, making it valuable to groups seeking control or freedom.
In the first game, Altaïr encounters an Apple of Eden during his missions in the Holy Land. The artifact becomes part of the wider conflict because Templars generally want to use Pieces of Eden to impose order, while Assassins oppose that form of domination.
The Apple is not the same object as every other Piece of Eden. The Staff, Sword, and Shroud are separate artifacts with different histories and abilities. “Apple of Eden” is therefore more specific than simply answering “Piece of Eden,” which names the artifact category.