Earlier straitera mentioned our normal 3D realm. I'm something of a physics buff, and read some advanced books from time to time, and watch related programs. Physicists are looking for explanations for relationships that don't seem to make sense in current theory, and in recent years some theoretical developments have been developed that may answer some of their questions, like string theory. One of the theories that would explain anomalies in gravitational observations is that there are as many as nine dimensions, six more than we can perceive with our human senses. Gravitational forces may be dispersing through these other dimensions, which would explain the anomalies.
A complicated way of saying that there is very likely much more to the world than we can see, and the paranormal experiences that have been described here may one day be explained by multiple dimensions that we can only occasionally perceive, under special circumstances. Our 3D senses may interpret these crossover events in ways that we are familiar with, hence the apparitions, which may actually be something completely different that our ordinary senses just can't handle.
On the other hand, even that wouldn't explain my grandmother visiting me in a dream on the night that she died, 500 miles away. I had never dreamed about her before, or since. I didn't know she had died until a couple of days later. In the dream, she let me know that she was happy again, eyes bright and shining, now relieved after a period of physical deterioration. The "new house" she showed me was an enlarged version of her casket, which looked like a railroad car to me in the dream. I told my mother about the dream and described the "railroad car" and it really freaked her out, because I had unknowingly described her casket. I settled her down by pointing out that grandmother was happy in the dream, and was letting us know that she was in a good place. Mother told me that grandmother had always had a special interest in me since childhood.
There may be more than nine dimensions...