In the Energy band image above, there are certain energy ranges where no electron states can exist. e.g. Between band1 and band2, there is a range of energy states which no electrons can occupy. These gaps between energy bands are called ‘forbidden gap’. However, the term energy gap/forbidden gap/bandgap generally refers to the forbidden energy ranges between valence band and conduction band. Band gap also represents the minimum energy required for an electron in the valence band to move to conduction band.
For a metal, valence and conduction bands overlap. i.e. there are many free electrons and it is very easy for a valence band electron to become a conduction band electron. Since the metal contains a large number of free electrons without any additional energy requirement, it works as a good conductor of electricity.
An insulator has a large forbidden gap, and it is not easy for valence electrons to become free electrons by jumping into the conduction band.
A semiconductor has a smaller forbidden gap between valence and conduction band, and electrons can move up to conduction band with a smaller amount of energy like light or heat. Energy provided by heat at room temperature is sufficient for this to occur and semiconductors conduct some electricity.