The atomic structure and energy gap between valence band and conduction band plays important role in deciding the conductivity of the material. Thus conductivity depends on number of free electrons, to carry electric current.
Conductors: Copper, Gold, Silver, etc. contain large number of free electrons. Thus they are known as good conductor of electric current. There is no gap between valence band and conduction band (i.e. no forbidden gap), as shown below.
When voltage is applied, the free electrons start moving through the conductor. Thus in Copper, Gold, etc. electrons from valence band get extra energy from applied P.D. and they easily jump into conduction band. Such electrons become free from nuclear force.
Insulator: Rubber, plastic, ceramic, glass, etc. contain extremely few free electrons (practically zero). The forbidden gap between valence band and conduction band is very high (about 5eV-10eV). Thus in such materials, all electrons are tightly bounded with nuclear force.
Semiconductor: It is an artificial material. Its conductivity is between conductor and insulator, hence it is known as semiconductor. A semiconductor becomes a perfect insulator at absolute zero temperature. However, when temperature increases, the electrons in valence band absorb heat and they jump into conduction band. So its conductivity increases (i.e. resistance decreases) with temperature.
This property of semiconductor is known as Negative Temperature Coefficient of Resistance (NTC). Commonly used semiconductors are Silicon (Si-14) and Germanium (Ge-32).
This NTC property of semiconductor is very useful in transducers like thermistors to measure the change in temperature. They are useful in medical and industrial instruments for temperature controlling systems.