Parallel Universe - As per String Theory their is a concept of Multiverse. The Multiverse theory implies that our universe is not one, many universes exist parallel to each other. These distinct Universes within the multiverse theory are called Parallel Universes.
Can it Exist - It may or may not, as String theory has not been practically validated yet. The Scientific Community is divided on the issue. It still is only a theory.
However before his Death Stephen Hawking who was not a Fan of the Multiverse Theory Co-authored a paper that scales down the Multiverse Theory and limits the amount of Parallel Universes that can exist, as the Cosmos is finite there cannot be infinite parallel universes. Thus Hawking did not completely disregard or scarp the The Theory of Multiverses.
Coming back to us common folks. For us String Theory or Multiverse are all concepts as of now, they may be proved in the future or they may not be in our life time. We can consider them to be real only when they are made a part of the school curriculum.