A MOSFET is a p-type substrate with two heavily doped n-type wells buried in it, one called the source and the other the drain. The surface between them stays p-type, so electrons cannot cross it and no current flows.
The gate is an electrode above that surface, separated from it by an insulating oxide. A positive gate voltage gathers positive charge on the underside of the electrode, and that charge pulls electrons in the substrate up to the surface through the oxide. The charge never crosses the oxide, so no current flows into the gate itself.
Once enough electrons have gathered, the surface turns n-type and the source and drain are joined. That path is the channel, and the gate voltage at which it joins up is the threshold. Above the threshold current flows; lower the voltage and it stops. Opening and closing a current with an electrode that never touches it is why the MOSFET is the switch inside every digital circuit.