The fictional device that lets characters access ancestral memories in Assassin's Creed is the Animus.
The Animus is a machine that reads genetic memories and presents them as interactive experiences. In the original game, Desmond Miles is placed in an Animus by Abstergo Industries so researchers can investigate the memories of his ancestor Altaïr Ibn-La'Ahad.
Although the device is used like a game interface, the series treats ancestral memory as information encoded in a person's genetic material. Modern-day characters can therefore investigate historical events without literally traveling through time. The Animus also explains why the games can move between historical settings and a contemporary storyline.
The Bleeding Effect is a side effect of extended Animus use, not the machine itself. Pieces of Eden are powerful artifacts, and the Observatory is a location and device connected to Black Flag. These are recurring franchise concepts but are not synonyms for the Animus.