The other world has a beautiful history as ancient as man. Many of our great myths are stories of events in another world, such as on Mount Olympus. Other worlds are found in favorite children's stories as in the Chronicles of Narnia by C. S. Lewis. In such a world, there are talking animals and trees. Another key difference is that time passes at a different rate. The Pevensie children live full, adult lives before returning to childhood, having missed little time during the reality that contains WW II. Similarly, when they return, they have not aged greatly but the world of Narnia has aged and changed greatly.
Authors and film makers tend to have great fun when surprising their readers and audience by the surprise twist that the plot takes place in another reality.
The magic of this genre is that anything in our world can be changed, for better or worse. We can live for a few hundred years, travel great distances, be able to move through time as we move through space. The Thursday Next series by Jasper Fforde offer a complex alternate reality in which time travel is possible, literary integrity is a crucial part of law and government, vampires and werewolves exist, dodo birds have been resurrected through cloning and so much more it makes my head spin. And all it takes is the gentle letting go of some law of reality and suspending it.
Of course, like all science fiction genres, alternate reality is not all fun and games. Parallel universes frequently threaten the universe of the main character's universe. And quite often his/her universe is quite like our own. An excellent and curious example is Isaac Assimov's The God's Themselves, which includes characters from both sides of an Electron Pump.
Do not be fooled by our "common sense" ideas about parallel universes. Quantum mechanics has widened our minds to the possibility. I must admit that quantum physics is exactly where I lost my firm on physics and resigned myself to Newtonian laws.
*One such variation is the alternate history sub-genre. I plan to get to this one later.