Short minilecture on science (because I
like science

)
That was a really good question and deserves a real answer. The short answer is there isn't really any empty space except in gases, which people of all sorts walk through daily, without a thought.
If you're allergic to science, please skip the long answer following.
The notion of matter as largely empy space arose in connection with the Borh model of the atom. This was conceived in 1912 if I remember my dates correctly. In this view, an atom was a tiny nucleus orbited by even tinier electrons. By far the largest part of the atom was empty space. The Bohr model worked very well for the simplest atom, the hydrogen atom, but it was soon realized that the picture didn't work for anything more complex. (It was still a tremendous advance, just given the relative cosmic abundance of hydrogen.) The first quantum theory circa 1926 put quietus to the Bohr model except as a schematic way of representing electronic structure of atoms on two dimensional paper.
In the modern view, rather fully developed since Linus Pauling's work on chemical bonding, we do not imagine electrons as specks of matter. In chemistry, where a better picture of electrons is vital to clear understanding, we think of "orbitals" instead. The orbitals are generally labeled the volume where the electron might be found.
The volumes of these orbitals collectively "fill" the volume of the atom. In unbonded atoms, the orbitals are called s, p, d or f orbitals when referring to their general shape (subscripts denote orientation and coefficients denot principle energy level.)
In bonded atoms, the orbitals extend between the nuclei, which is what constitutes the bond. The basic configurations are pi or sigma orbitals. But it is possible and sometimes desirable to conceive of the orbitals as taking a shape specific to the molecular. This might ring a bell as Molecular Orbital theory of molecular structure (as opposed to the VSEPR theory.)
Middle school and high school science teachers have confused people by resurrecting the Borh model inappropriately. They've also confused people by telling students atoms and molecules are widely separated in gases (true,) slightly separated in liquids and in contact in solids. These last two are not true, which is the confusion. Traditionally the sequence of atomic models is brought into science classes as an historical example of the process of scientific discovery. (In practice, there doesn't seem to be enough historical detail or narrative to serve that purpose. But the Bohr model's attractive simplicity seems to stick in place of the quantum theory, for the good reason quantum theory isn't actually taught.)
All unbonded atoms are separated, by quantum effects if nothing else. In liquids, the intermolecular forces keep the atoms or molecules from separating like the particles in gases. Liquids have a definite volume. But the particles can move freely, so this phase has no definite shape.
Liquids are essentially incompressible. That's why hydraulics work!
The particles in solids are not literally in contact either. The same electron repulsion responsible for elastic rebound in gases prevents this in solids. But the intermolecular forces in solid are strong enough to prevent free movement from place to place, albeit unable to prevent rotation and vibration. Rotation and vibration are why there is contamination in crystals, as foreign particles slowly migrate into the structure. It is also why crystals or other solids can deform over time, depending on conditions. Wax, firn in glaciers, mantle rock, antique plate glass, for examples.
Since compressibility has to do with electron repulsion, can't atoms themselves be compressed by something? Of course. If gravity is sufficiently strong, it can overcome electron repulsion between atoms. The electrons are forced into the nucleus where they sort of combine with protons to become neutrons (skipping over the nuclear physics here, if you don't mind.) This state is called electron degeneracy. It is what produces a neutron star. If you turned your body into that kind of matter, it would be dense enough to pass through ordinary solid matter like a human body walking through air. It would also be lethal. Not a useful power to have.