Electrical conduction is the movement of electrically charged particles through matter. The movement can form an electric current in response to an electric field. The underlying mechanism for this movement depends on the material.
Conduction is well-described by Ohm's Law, which states that the current is proportional to the applied electric field. The ease with which current density (current per area) appears in a material is measured by its conductivity.
Metals
Metals are good conductors because they have unfilled space in the valence energy band. In the absence of an electric field, there exist electrons travelling in all directions and many different velocities up to the Fermi velocity (the velocity of electrons at the Fermi energy). When an electric field is applied, a slight imbalance develops and mobile electrons flow. Electrons in this band can be accelerated by the field because there are plenty of nearby unfilled states in the band.
Semiconductors
A solid with filled bands is an insulator, but at finite temperature, electrons can be thermally excited from the valence band to the next highest, the conduction band. The fraction of electrons excited in this way depends on the temperature and the band gap, the energy difference between the two bands. Exciting these electrons into the conduction band leaves behind positively charged holes in the valence band, which can also conduct electricity. See semiconductor for more details.
In semiconductors, impurities greatly affect the concentration and type of charge carriers. Donor (n-type) impurities have extra valence electrons with energies very close to the conduction band which can be easily thermally excited to the conduction band. Acceptor (p-type) impurities capture electrons from the valence band, allowing the easy formation of holes. If an insulator is doped with enough impurities, a Mott transition can occur, and the insulator turns into a conductor.
Superconductors
In metals and certain other materials, a transition occurs at low temperature to the superconducting state. By an interaction mediated by some other part of the system (in metals, phonons), the electrons pair up into Cooper pairs. The bosonic Cooper pairs form a superfluid which has zero resistance.
Source: Wikipedia
