Atoms in a solid crystal pack very closely together to share their electrons. Their shared electron orbits merge into large continuous bands of allowed energy. The bottom band is called the valence band, and it is totally full.
The upper band is called the conduction band, and it is usually empty. The forbidden zone is the totally empty space resting between these two bands. Electrons are completely blocked from resting anywhere inside this empty gap region.
To conduct electricity, an electron must absorb enough energy to jump the gap. Metals do not have a forbidden zone because their energy bands simply overlap. Insulators have a massive forbidden zone that normal electrons can almost never cross.
Semiconductors have a narrow forbidden zone that a little heat or light can bridge. A common misconception is that the forbidden zone is an actual physical empty space. The zone is strictly a measure of energy, not a physical location inside the crystal.
Scientists can purposefully add chemical impurities to a semiconductor to change its behavior. This doping process adds new stepping stones inside the previously empty forbidden zone. These new stones make it much easier for eager electrons to jump the gap.