Semiconductors are defined to have conductivity in between an insulator and a conductor. Due to this property, semiconductors are very common in every day electronics since they likely will not short circuit like a conductor. They get their characteristic conductivity from their small band gap. Having a band gap prevents short circuits since the electrons aren't continuously in the conduction band. A small band gap allows for the solid to have a strong enough flow of electrons from the valence to conduction bands in order to have some conductivity.
Electrons in the conduction band become free from the nuclear charge of the atom and thus can move freely around the band. Thus, this free-moving electron is known as a negative charge carrier since having the electron in this band causes electrical conductivity of the solid. When the electron leaves the valence band, the state then becomes a positive charge carrier, or a hole.
Pure semiconductors in which its properties are solely based off of the material itself. Here, the number of electrons in the conduction band equal the number of holes in the valence band. Theses semiconductors are also known as i-types.
Impure semiconductors that have been "doped" in order to enhance its conductivity. There are two types of extrinsic semiconductors: p-type and n-type. A "dopant" atom is added to the lattice in order to draw electrons from the valence band. This atom is referred to as an acceptor. As more acceptors are added to the lattice, the number of holes will begin to exceed the number of negative charge carriers, eventually leading to a p-type (positive type) semiconductor. N-type semiconductors have a large number of donors, "dopant" atoms that donate electrons to the conduction band.