The quantum mechanical principle, formulated by Pauli, that no two identical fermions may occupy the same quantum state.
Fermions of the same species form totally antisymmetric states. In the two-particle case:
If both particles occupy the quantum state |ψ>, the state of the entire system is |ψψ>. Then
so such a state does not occur. This is readily generalizable to the case of more than two particles.
The Pauli exclusion principle is the reason you do not fall through the floor.