Carl Sagan explains it well...
When I was a kid and laid down on the grass at night and studied the stars, I often thought about how vast it is. Too vast for us to understand. Are we seeing the universe as it really is, or just dots and bits of something even bigger? What if our earth and other planets are nothing more than cells that make up something inconceivably larger? Something like if the cells in your body see each other, but would not know they were part of a bigger thing called a human being. They have no perspective to understand that concept. We look at planets and stars and think that's it, a lot of objects floating in a giant space.
Consider this: We have 2-dimensional things in our world, such as images on photographs and TV screens. If you were from another planet and visited us, it would seem quite strange that a human could study a box for hours at a time and find entertainment, but it is the images and added soundtrack that stimulate our mind, so we watch the TV screen. If you were inside the TV screen, all you would see around you are the things in your periphery, width and length, but there is no height, so you have no perspective that there are 3-dimensional beings outside of your TV screen watching you.
Now, imagine if you will that if we in the 3-dimensional world of height, breadth, depth, width, mass, can be entertained by watching 2-dimensional activity, imagine what those in the next dimension might feel about our 3-dimensional world? Whereas we use paper and pen to conceptualize in 2-D form but see it as only representational and not real, might the next dimensionals use the third dimension to conceptualize and use it as representation but not reality? We can co-exist with the second dimension in the same space, and so we might be sharing our space with the next dimension--well, almost certainly!
When we can conceive of other dimensions simultaneously occurring, we can also perhaps explain some things that have baffled us, such as apparitions appearing and disappearing, UFOs arriving and departing in ways that appear to defy known laws of physics. How about poltergeist movement of objects? Something like that Carl Sagan explanation of a 3-dimensional being grasping a 2-dimensional being and lifting him out of his context. It might be that the item was not thrown by unseen forces, but perhaps manipulated by the next dimension and to us it appeared to occur quite magically. I'd compare this to dripping a drop of paint on a photo image and having Mr. Photo Image go "where did that come from? It just appeared in my world."
What is even more intriguing about these concepts is that if we did catch glimpses of other dimensional “things,” we are very likely only seeing the portion of it we can conceive of in our 3rd dimension:
If you were in a 1-dimensional world, you could see in front and behind you, but not to the sides or up and down.
If you were in a 2-dimensional world, you could see in front and back and to the sides, but not up and down.
If you are in a 3-dimensional world (which we are), you could see front and back, sides and up and down.
I hope I got you thinking a bit more and wondering why I put this on a ghost hunting theories site. It is entirely possible that what we consider the afterlife is really freeing ourselves from the 3-dimensional body to be all-knowing, all-encompassing. We dominate over the 2-D world and we can do so because we can tackle it from all its dimensions, but what can another dimension do to our 3-D world? Could it be that it is a universe that can conceive of everything while having no need for mass as we know it? Does just a physical form of us get shed so we might go onto be unencumbered by such things and be able to conceptualize the next dimension? This is very much like what near-death experiencers describe; that was the real world, this world they came back to is the fake one.
Wouldn't it make it very hard indeed for the next dimension to interact with us in a way we can understand? If we put a drawing on a piece of paper next to another doodle we did earlier, it sees that another of its kind is nearby, but knows nothing of how it got there or why minutes later it was erased from existence. This is sort of like seeing a glimmering apparition for a few brief seconds to have it disappear or even a UFO. We only see part of this next dimensional being because we can only view it in our 3rd dimensional reference, just like that 2-dimensional drawing only saw another dot nearby it and recognized a dot as "his kind" even though it was a human standing there. With no ability to conceptualize height, it was simply another one of his being friends; the part of him he has the concept to recognize.
What part of the next dimension can we not visualize?
So, is Heaven the next dimension?
Using our own world as a comparison, imagine that we draw up a sketch of a machine we want to build. We plot it out on 2-dimensional form and then build it into the 3-dimensional form. Our 2-dimensional concept became a 3-dimensional reality. Now, image that there is a "God" and this God sends one of His out to greet us and we see him only in his 3-dimensional form because that is the only way we can view things (like that poor 2-dimensional fellow would only see us 3-dimensionals as a dot). So, this man has abilities to make things appear and disappear (like that 3-dimensional man moving around the 2-dimensional objects) and we call this man a God and name him Jesus or other visionary. What if when a person passes on, he is actually being represented in the next dimensional plane as that drawing we made became a machine we built. We are nothing more than a concept in the third dimension but we become a reality in the next dimension... afterlife.
If this has piqued your interest and you want to go further on such explorations, here's some great sources -
Fantastically understandable video example
Great written explanation.
A great book by Marie Jones "PSIence"