Quantum numbers are unique combinations of information for a particular electron that we can use to explain its behaviour.
Quantum numbers are like a unique identity for each electron in an atom. They also explain a lot about why electrons do what they do, like pairing up with others. There are four numbers:
Fermi exclusion principle states that no two electrons may have the same combination of quantum numbers. Two electrons in an orbital automatically have the same distance, shape and orientation of orbitals, and so they must have opposite spins - this is how electrons form pairs. One spins one way, one spins the other.
Quantum numbers can be used for other applications too, and explain much about behaviour. Put simply, though, they are unique sets of numbers that describe an electron and set it apart from all the others.