The fictional device linking Assassin's Creed's present-day characters to ancestral memories is the Animus.
The Animus is a machine that allows a person to experience genetic memories inherited from ancestors. In the first game, Desmond Miles is forced to use it so the Abstergo organization can investigate the life of his ancestor Altaïr Ibn-La'Ahad. The device provides the narrative bridge between modern settings and historical adventures.
The series later introduces different Animus models and related interfaces. Abstergo develops the technology for its own research and commercial projects, while the modern Assassin network uses adapted versions to study memories and uncover information. The games present genetic memory as a fictional concept rather than an established scientific ability.
The Animus is not the same as an Apple of Eden. Apples are powerful First Civilization artifacts that influence minds, while the Animus is the machine used to access memories. Another related term is the Bleeding Effect, which describes skills and psychological effects that can pass to an Animus user through prolonged exposure.