Diagram illustrating how electronic band structure of a solid comes about by the hypothetical example of a large number of carbon atoms coming together to form a diamond crystal lattice.  The graph (right) shows the energy levels of the atoms as a function of the spacing between atoms.  When the atoms are far apart (right side of graph) each atom has valence atomic orbitals p and s which have the same energy.  However when the atoms come closer together their orbitals begin to overlap.  The Pauli Exclusion Principle dictates that no two atoms in a molecule can have electrons with the same quantum numbers, so each atomic orbital splits into N molecular orbitals each with a different energy, where N is the number of atoms in the crystal.  Since N is such a large number (~1022) adjacent orbitals are extremely close together in energy  (~10-22 eV) so the orbitals can be considered a continuous energy band.a is the atomic spacing (lattice constant) found in an actual crystal lattice of carbon atoms (diamond lattice) so the band structure at that spacing is the one found in diamond.  At that spacing the orbitals form two bands, called the valence band and conduction band, with an energy gap of 5.5 electron volts (eV) between them.  The valence electrons fill the lower band.  Electrons in this band are not mobile; while electrons in the higher conduction band can travel through the crystal from atom to atom, and thus serve as charge carriers to conduct electricity.   Since the 5.5 eV band gap is much larger than the thermal energy of most electrons in the crystal, very few electrons acquire the energy to jump the gap and become conduction electrons.  This is why diamond is an electrical insulator.
The shape of the graph (right) is only approximately correct.  It also only shows the band structure of the outer (valence) electrons of the atoms (in carbon the 4 2p and 2s electrons).  The orbitals of the inner electrons do not overlap to a significant degree, so their bands are much  narrower.
Own work
Chetvorno