What are quantum numbers?

A number which occurs in the theoretical expression for the value of some quantized property of a subatomic particle, atom, or molecule and can only have certain integral or half-integral values.

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of electrons, the quantum numbers can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom