People have an experience that is like...being outside of their body. That's where the English word "ecstasy" comes from, it means "ex-stasis" or "outside situation/position".
In the materialistic way of thinking, this is impossible. How can you experience something that is not within your senses? If you see your own body, you must be using vision, which means that you're using your eyes, which means you have a body with eyes. So, you are not out of body.
But if you know that you are not looking at a mirror, then how to explain that? Like Eissy said above, some people conclude that we must have another body. Some people call it the Subtle Energy Body, or the Astral Body, or the Etheric Body...or, yes, the Soul.
The experience is real. I have had a number of out-of-body experiences myself. However, the interpretation of it still needs more data, as well as the empirical uses of such an ability. For example, I shuffled a pack of playing cards and put them on the top of the bookshelf without looking. When I go out of body, I try to look at the cards. They have never been correct.
However, I have had experiences of being outside of my physical body, that was not a dream or imagination. Robert Monroe describes it better and wrote a lot of books about it. If I recall correctly, Robert Monroe was a test subject with Dr. Charles Tart who investigated this sort of travel. It was an anonymous test subject that succeeded with a similar experiment that I described, but with numbers, the specific number was 25132. But if even Monroe couldn't make the data significant, then it's difficult to navigate even though the experience is very real.