Hole conduction can be explained by the use of the following analogy. Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so they jump over the back of the seat into an empty row, and walk out. This empty row is analogous to the conduction band, and the person walking out is analogous to a free electron.
Now imagine someone else comes along and wants to sit down (the empty row has a poor view, no one wants to sit there). Instead, the person next to the empty seat moves along and sits in it, leaving an empty seat one spot closer to the edge. The next person follows, and the next. One could say that the empty seat moves towards the edge of the row. Once the empty seat reaches the edge, the new person can sit down.
But in the process, everyone in the row has moved along. If those people were charged (like electrons), this movement would constitute conduction. This is how hole conduction works.
Instead of analysing the movement of an empty state in the valence band as the movement of billions of electrons, physicists propose an imaginary particle called a "hole". In an applied electric field, all the electrons move one way, so the hole moves the other way. The physicists therefore say that the hole must have positive charge - in fact, they assign a charge of +e - precisely the opposite of the electron charge.
Using Coulomb's law, we can calculate the force on the "hole" due to an electric field. Physicists then propose an effective mass which will relate the (imaginary) force on the (imaginary) hole to the acceleration of that hole.
It turns out that effective mass is fairly independent of velocity or direction, which means physicists can (in some cases) pretend that the hole is simply a positive charge moving through a vacuum, with a mass of, say 0.36me (a value typical for silicon).
See also: electrical conduction, semiconductor, bandgap, effective mass
An alternate meaning for the term electron hole is used in computational chemistry. In coupled cluster methods, the ground (or lowest energy) state of a molecule is interpreted as the "vacuum state" — conceptually, in this state there are no electrons. In this scheme, the absence of an electron from a normally-filled state is called a "hole" and is treated as a particle, and the presence of an electron in a normally-empty state is simply called an "electron".
This terminology is almost identical to that used in solid-state physics. The major difference is in the theory used to describe each type of hole. A solid-state hole is seen as a free particle with an effective mass, possibly with incremental improvements on that model. A physical chemistry hole is analysed by using the Schrödinger equation directly.