The device used to access genetic memories in Assassin's Creed is called the Animus.
The Animus allows a user to experience ancestral memories encoded in their genetic material. In the first game, Desmond Miles is forced to use Abstergo's machine to relive the memories of Altaïr Ibn-La'Ahad. Later stories show other versions of the technology used by Abstergo, the Assassins, and entertainment companies.
The machine gives the series its characteristic movement between a modern storyline and historical settings. It also supports the fictional concept of the Bleeding Effect, in which repeated exposure can transfer skills or behavioral traits to the user.
The Apple of Eden is a separate First Civilization artifact, not the memory machine. Helix is the name of a later virtual-reality entertainment platform, while the Bleeding Effect describes a consequence of Animus use.