In the first Assassin's Creed game, the device that lets Desmond relive ancestral memories is the Animus.
The Animus is a machine developed by Abstergo Industries. It uses a person's genetic memories to reconstruct experiences from ancestors, allowing Desmond Miles to live through the memories of Altaïr Ibn-La'Ahad. This technology provides the transition between the modern-day storyline and the historical missions.
The game presents genetic memory as a fictional inherited record rather than a real scientific capability. Desmond's sessions also produce side effects associated with the Bleeding Effect, through which skills and perceptions from an ancestor begin influencing the user.
The Apple of Eden is different: it is a Piece of Eden, an ancient artifact that can influence minds. Eagle Vision is a perception ability used by certain characters. Neither is the machine that accesses Desmond's ancestral memories.