There is no empty space in the world.
Within the confines of quantum electrodynamics, all particles are constantly talking to each other through exchanges of virtual photons. Within this "vacuum" there exists an infinite number of particles going into existence and out of existence within the time defined by the heisenburg uncertainty principle. As such in reality there is no empty space.
Also this relates to the Higgs boson and why LHC in CERN was made. It is believed that the world is made up of a super fluid of these boson, much like the quantum theory of super conductors. This is the modern concept of ether that many people might have heard about being debunked many years ago. read http://en.wikipedia.org/wiki/Michelson–Morley_experiment for more...
So in a simple answer to your question, the electric force, the long distance force of all the electrons around the nucleus of the atom talk to each other and basically tell the other electrons to back off. Since the force goes up inversely with the square of the distance, this force becomes very very very large as they get close. As such we are all floating around and touching things based on electronic repulsion or attraction...
Long winded answer and a little rambling but I hope you get the gist. The main thing to know is electronic repulsion, and there is no "vacuum" in the case of emptiness...the smaller you go in distance and time, the more crazy the world becomes!