The first state has a large electron charge density between the atoms, the second one has a node in the wave function between the atoms and hence a small charge density. In the first case the repulsion between the nuclei is strongly screened, and the energy of this state is lower. Note that due to the symmetry in perturbation theory for large separations the first state decreases in energy by the same amount as the second one increase. The names of the states are bonding and anti-bonding state, for obvious reasons. This explains figure 8.1.
Divalent materials are metals because the s and p bands overlap.
For N atoms we can form many combinations. States can be bonding between a certain number of neighbor pairs of atoms and antibonding between the remainder. Many different energy values are possible, they all are in between the energy of a state that is bonding everywhere and a state that is antibonding everywhere. The states are discrete, but when N is large like in a solid, it is a very good approximation to take the set of states as continous. Such a set of continuous levels is called a band.