For electricity to flow is for electrons to move. That would seem to mean any material containing electrons ought to conduct — yet in reality some materials conduct and some do not. Where does that difference come from?

The key is that the energies an electron is allowed to have are fixed in discrete steps. In an isolated atom, an electron's energy takes one of a set of separate levels. But once atoms line up by the billions in a crystal, those levels shift slightly against one another and overlap, spreading out into a band with real width. This is called an energy band.

Two bands matter. The valence band, packed full of electrons that therefore cannot move, and above it the conduction band, where electrons are free to roam. Between the two lies a gap in which no electron can exist. That gap is the band gap.

In a conductor — copper, aluminum — those two bands overlap, or there is no gap between them at all. Electrons are always free to move, so apply a voltage and current flows immediately.

In an insulator — glass, rubber — the gap is wide, 5 eV or more, and at room temperature an electron essentially never jumps across it. That is why it does not conduct.

A semiconductor sits in between. Silicon's band gap is about 1.1 eV, and that is exactly the right size: at room temperature most electrons cannot make the jump, but give them a little heat, light, or voltage and they can. The property of "conducting or not conducting, controllable from outside" is born out of that very in-betweenness.