A range of allowed energies of single-electron states in a solid, particularly a metal.
Energy bands are an exclusively quantum-mechanical phenomenon.
The origin of energy bands can be considered from two opposing standpoints. If two identical atoms are brought together, the interaction between them gives rise to two levels with slightly different energies for each single electron level of the isolated atom. As the number of atoms in the system increases, the energy levels spread still further until, for the large number of atoms close together in the solid state, the energy levels have spread into a band that has such a small gap between individual levels that it is effectively a continuous range of states. Those wavefunctions with wavelength close to the interatomic spacing will be most affected, and an energy gap opens up in the allowed energy states. Either picture is an approximation, and sophisticated techniques are required to calculate the band structure of a solid.