A paraverse is a parallel universe.
The many-worlds interpretation (MWI) of quantum mechanics says that whenever the universe is confronted by a choice of paths at the quantum level, all possible outcomes of quantum measurements are physically realized in some other or universe, splitting into multiple universes or parallel universes. With the multiverse hypothesis, MWI views time as a many-branched tree, wherein every possible quantum outcome is realized. This is intended to resolve paradoxes of quantum theory such as Schrödinger's cat, since every possible outcome of a quantum event exists in its own universe.
With quantum immortality, the MWI implies that we may be able to live virtually forever. For example, suppose you are in an electric chair. In almost all parallel universes, the electric chair will kill you. However, there is a small set of alternate universes in which you somehow survive—for example an electrical component may fail when the executioner pulls the switch. Somehow if you are able to manipulate the outcome that your quantum self takes, you will be able to live virtually forever.