When one studies the properties of atoms, one found that the reality is far stranger than anybody would have invented in the form of fiction. Particles really do have the possibility of, in some sense, being in more than one place at one time.
Now, what space ultimately is - I should confess, I think most physicists believe - we don't yet know.
Our best theory of describing space at a fundamental level is probably string theory.
In the context of general relativity, space almost is a substance. It can bend and twist and stretch, and probably the best way to think about space is to just kind of imagine a big piece of rubber that you can pull and twist and bend.
Space is certainly something more complicated than the average person would probably realize. Space is not just an empty background in which things happen.