Each silicon atom shares its four valence electrons with its neighbours, building a stable crystal. Thermal jitter can knock an electron out of a bond, leaving a free electron and a hole behind. After a while the electron falls back into the hole and the pair disappears.
Add a trace of pentavalent phosphorus and one electron is left over, with no bond to fill. That electron leaves its atom and carries charge as it moves. The phosphorus that let it go stays fixed in the lattice as a positive ion.
Add trivalent boron and one electron is missing, leaving a vacancy in a bond: a hole. Electrons hop in from neighbouring bonds one after another, so the vacancy travels the other way. The hole therefore behaves like a particle carrying positive charge.
At the junction electrons and holes meet and vanish, leaving a depletion layer with almost no carriers. A forward voltage (＋) narrows that layer, and current starts to flow past roughly 0.6 V. A reverse voltage (−) widens it and almost no current flows.
A positive gate voltage pulls electrons toward the surface through the insulating oxide. Above the threshold the channel joins up and current flows from source to drain. Opening and closing that channel is the switch inside every digital circuit.