The fictional machine that lets users experience ancestral memories in Assassin's Creed is the Animus.
The Animus is a device that reads genetic memories inherited through a person's DNA. In the first game, Desmond Miles is forced to use an Animus by Abstergo Industries so researchers can explore the memories of his ancestor, Altaïr Ibn-La'Ahad. The machine provides the framework for moving between a modern storyline and historical gameplay.
Although the series describes the memories as genetic, the Animus does not literally send users into the past. It reconstructs experiences from ancestral memory and presents them as an interactive simulation. Synchronization measures how closely the user follows the remembered events, while the Bleeding Effect describes skills or memories spilling into the user's mind after prolonged exposure.
The Apple of Eden is different: it is a powerful Isu artifact, not a memory machine. Abstergo develops and operates Animus technology for research, control, and entertainment, and later versions appear in several forms throughout the franchise.