Original: This "antisymmetric wavefunction" behavior implies that fermions are subject to the Pauli exclusion principle, i.e. no two fermions can occupy the same quantum state at the same time.
Simplified: Fermions are special because you can not put two of them in the same place at the same time. This is because the Pauli exclusion principle says that no two fermions can have the same quantum numbers, such as spin numbers, at the same time.