The fictional technology that lets characters relive genetic memories in Assassin's Creed is the Animus.
The Animus is a machine developed by Abstergo Industries. It allows a user to access ancestral memories encoded in genetic material, then experience those memories as an interactive simulation. The modern-day sections of the games use this device to connect contemporary characters with historical Assassins and Templars.
The technology does not literally transport a person into the past. Instead, the user enters a reconstructed memory and can explore it through the perspective of an ancestor. The games also use the Animus to explain gameplay systems, including synchronization, replaying memories, and correcting deviations.
The Bleeding Effect is different: it is a side effect of prolonged Animus exposure, in which a user may acquire skills or memories from an ancestor. Helix is another fictional interface and entertainment product, not the original machine's general name.