A hole is a missing electron in an otherwise filled valence bond, treated as a mobile particle carrying positive charge . Not a real particle, just the absence of an electron, but it moves, carries current, and is bookkept exactly like a positive charge, so we treat it as one.
Where holes come from
In a silicon crystal every atom shares its four valence electrons in covalent bonds. When thermal energy (or light, or a dopant) removes one electron from a bond, promoting it to the conduction band, the bond is left with a vacancy. That vacancy is the hole. Creating a free electron always leaves a hole behind, so holes and electrons appear together as electron–hole pairs, and they disappear together when a free electron drops back into a vacant bond (recombination).
Why a hole moves and acts positive
The hole itself doesn’t move, electrons do. A neighbouring bound valence electron can hop into the vacancy without being freed into the conduction band. When it does, the bond it filled is now complete, but the bond it left is now empty: the vacancy has shifted one site over, in the direction opposite to the electron’s hop.
Repeat this many times and the vacancy travels through the crystal by successive electron hops between bonds. The net result is a flow of positive charge in the direction of vacancy motion. Rather than track the cooperative motion of many bound valence electrons, we package it into one fictitious particle (the hole) with charge that drifts and diffuses like a real carrier. Much simpler, and how semiconductor analysis treats it.
Holes as charge carriers
A doped semiconductor conducts via two carrier types in parallel: free electrons (charge ) and holes (charge ). In an n-type material electrons vastly outnumber holes; in a p-type material holes are the majority carrier. Their concentrations are linked by the Mass-action law . The two carrier types respond oppositely to an electric field, electrons drifting one way and holes the other, both contributing current in the same direction. That’s what makes a PN junction, and therefore every diode and transistor, work.