Usually one is led to think of an electron moving from the valence band to the conduction band as an electron leaving the atom it is bound to in the lattice, and becoming free to move, while leaving apart a hole that is free to move as well. How accurate is that picture, how useful is it, and what does it really mean?
If I understand correctly, the (energy eigen)states in the valence band are such that the electron is more tightly bound to atoms in the lattice than it would be in an individual atom, though for every single state the electron is found with equal probability at every nucleus in the lattice, i.e. individual electrons are not bound to specific sites.
Electrons in the conduction band are more weakly bound than they would be in a single atom. Is it the particular combined state of all electrons that causes the probability to find an electron at some lattice point to be lower than at others (location of a hole), and the probability of finding an electron at some non-lattice point to be higher than at others (location of an electron that is free to move/not bound to any atom)?
Does a change in the state of one electron to a state that is nearby in the conduction band correspond to the movement of a free electron, and that of a state in the valence band to a nearby state to the movement of a hole?
I'll try to be more specific, assuming that my understanding outlined above is more or less correct. When introducing bands, usually a picture is drawn in which there are two very densely spaced ranges of energy eigenfunctions that can each be occupied by one (or two, when not taking spin into account) electrons. The combined ground state would have the valence band fully occupied, and the conduction band empty.
When an electron gets excited from the valence band to the conduction band, this is described as the electron moving to a higher energy level, leaving the lower energy level free, but at the same time as an electron leaving a fixed position (in the crystal lattice), and becoming free to move.
Since the energy eigenstates don't localize the electron at any particular lattice site, the equivalence of these two interpretations seems not at all obvious, nor how it could work. Is it that there is a change of basis in which the electrons are localized, and in which interchanging the coefficient of a state in the valence band with that of a state in the conduction band corresponds to a displacement of an electron. Does this have to do with the Bloch states and Wannier states mentioned in the answer to the question that John Rennie referred to in his comment?