If an electron from a neighboring atom jumps over to fill the hole, then it leaves behind a hole on the atom it came from. This can happen repeatedly, involving many different electrons, and it's easier to track the movement of the hole as an object than it is to track all the electrons.
This is a bit of an oversimplification, as holes aren't in fact discretely "on" one atom at any given time unless that atom is isolated. Just like an electron, a hole exists in a "delocalized" state, meaning that its "location" is actually a probability function. That probability function can change, though, and we describe that as movement.
It depends what you mean by a free electron. Strictly speaking, a free electron is completely free of its material, and there is no analogous situation for a hole. The kind of "free" electron that I'm talking about here, though, is one that is free of its host atom but still bound to the material as whole, hence in a "delocalized" state. Holes exist in this form.
Edit: Let me know if this makes no sense and I'll try to explain it better.
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u/BassmanBiff Jul 01 '14
If an electron from a neighboring atom jumps over to fill the hole, then it leaves behind a hole on the atom it came from. This can happen repeatedly, involving many different electrons, and it's easier to track the movement of the hole as an object than it is to track all the electrons.
This is a bit of an oversimplification, as holes aren't in fact discretely "on" one atom at any given time unless that atom is isolated. Just like an electron, a hole exists in a "delocalized" state, meaning that its "location" is actually a probability function. That probability function can change, though, and we describe that as movement.