The fictional device that lets Desmond Miles relive ancestral memories is the Animus.
In the Assassin's Creed series, the Animus is a machine that reads genetic memories and presents them as interactive experiences. Desmond Miles uses it to access the memories of ancestors such as Altaïr Ibn-La'Ahad and Ezio Auditore. The device provides the framework connecting modern-day characters with historical adventures.
The Animus is operated by Abstergo Industries, the modern organization linked to the Templars. Later stories introduce different versions and related systems, including the Helix, a consumer-oriented entertainment product associated with Abstergo.
The Animus is not the same as an Isu artifact such as the Apple of Eden. Nor is the Bleeding Effect a machine: it is the side effect of prolonged Animus exposure, through which users can acquire skills or memories associated with the people they experience. These distinctions are important because the series uses several overlapping science-fiction concepts.