The term parallel dimension or universe lacks definition. There are many dimensions and just as many universes. It's difficult to define a term that science has not yet explored or discovered. When we look up in the sky on a star filled night, we see other star systems clustered together. These stars look so close to one another, it seems they must be touching but they are in fact, extremely far apart. If we were in a star ship traveling toward one these star systems, the closer we got to then, the further away they would be perceived. As we got closer, the singular stars would disappear altogether. Then, as we get even closer to them, they would once again, slowly begin to re-appear.
The universe is a sea of particles, one linked to the other. Some of them we can see because they are within a boundary or spectrum that we are able to perceive. It is the electron that we perceive. However, an electron by itself is way too small to be perceived by the human eye or even by modern technology but we can perceive the electron when the electron flow is dense! Like the star clusters in the sky, we perceive matter when it is dense enough for us to perceive.
Electrons flow through space in conduits, just like electrical wires. Electrons flow through all matter in varying densities. The only thing that the electron cannot flow through is another electron. The electron, the smallest and most dense particle that exists, is too dense to allow anything to flow through it.
Human physiology only allows us to perceive matter at a specific density, a specific pressure spectrum (or dimension). If we were able to perceive matter in multiple spectrums, then matter would not have definition. If humans could view multiple pressure spectrums or dimensions, we would not be able to tell anything than what we could perceive from the rest of space. Just because we can't perceive something doesn't mean it doesn't exist.
Dimensions are other spectrums that exist outside of our ability to perceive them because of their specific density. The matter that exists in other dimensions is the same matter that we perceive in our dimension. Other dimensional matter is all around us.
If you wave your hand in the air, your hand is passing through other dimensional matter. It is just as solid as the ground you walk on but the electron conduits in your hand pass between the electron conduits of the other dimensional matter.
The earth is surrounded by other dimensional planets, "our planetoid cluster", which rotates through the earth and through us! These other dimensional planets extend out into space, one linked to the other, rotating through one another and orbiting together.
Scientists look out into space with giant telescopes and they see stars appear and disappear. There are many theories about this occurrence. There are stars dying and being born or being sucked into black holes. However, these are just theories and will remain theories until other evidence is discovered.
Planets do not orbit in a linear fashion. Stars, planets and particles all orbit in the same manner; down and around in a cork screw manner. As we fall through space, we go from a high pressure to low and back to high. As our solar system comes under more and more pressure as it orbits down through space, all of the particles contract as they come under higher pressure. We don't see it and we don't feel it because everything is moving relative to one another. However, if someone on another planet out in space were to be exploring our sun through a telescope, there would come a time when our sun would blink out as it contracted to a point that it could no longer be seen from that distance. These alien observers might think that our sun had died or gone into a black hole. However, this would not be the case. Our sun would simply be going into another pressure spectrum or dimension.