The gap between the bands is about 1 eV. At finite temperature there will be some carriers in the conduction band. The book shows that the amount is proportional to which is about for Si. Hence the number of electrons in the conduction band is small, but since there are so many electrons in total it still adds to a measurable amount of electrons, and hence we can measure the current. In addition, we have empty states in the valence band. This also allows conduction.
Electrons can jump into an empty spot driven by the electric field.
This cascade of electron jumps will have the visual effect of the vacant spot moving in the oposite direction from the electrons. We model this behavior by focussing on this vacancy and assume it is like a particle. Since it is a missing electron it has a positive charge, and indeed it moves in the direction of the electrical field. Such a fictitious particle is called a hole . Keep in mind, that in reality it is always the electrons that are moving.