The machine used to experience ancestral memories in Assassin's Creed is called the Animus.
In the series, the Animus uses a person's genetic memories to reconstruct events experienced by their ancestors. Modern-day characters enter the machine and interact with historical simulations, allowing the games to move between contemporary scenes and major historical settings.
The Animus is a fictional device, but the series presents it as a technology developed by the fictional Abstergo Industries. Early games center on Desmond Miles, whose ancestry gives him access to memories associated with Altaïr, Ezio, and Connor. Later stories introduce other users and variations of the system.
The term should not be confused with the Bleeding Effect. The Bleeding Effect is a consequence of extended Animus exposure, in which a user may acquire skills or memories from an ancestor. The Animus is the machine itself, while the Bleeding Effect is an in-universe side effect.