The virtual-reality machine used by Abstergo in Assassin's Creed is called the Animus.
The Animus allows a modern subject to access genetic memories inherited from ancestors. In the series' central premise, this technology lets contemporary characters experience reconstructed moments from the past without physically traveling through time. Abstergo Industries uses the machine for research and for locating information connected to the Pieces of Eden.
The Animus is not the same thing as Eagle Vision, which is a perception ability used by many protagonists. The Bleeding Effect is also different: it is a consequence of prolonged Animus exposure that can cause users to retain skills or behaviors from an ancestor. The Apple of Eden is a Piece of Eden, not a machine.
Although the series treats genetic memory as science fiction, the Animus provides its recurring structure. It explains why games can move between historical settings and a modern storyline, and it allows the player to control an ancestral character while the contemporary subject remains connected to the simulation.