It can be seen that in some conductors, such as ionic solutions and plasmas, there are both positive and negative charge carriers, so an electric current in them consists of the two polarities of carrier moving in opposite directions. In other conductors, such as metals, there are only charge carriers of one polarity, so an electric current in them just consists of charge carriers moving in one direction.
There are two recognized types of charge carriers in semiconductors. One is electrons, which carry a negative electric charge. In addition, it is convenient to treat the traveling vacancies in the valence band electron population (holes) as the second type of charge carrier, which carry a positive charge equal in magnitude to that of an electron.
When an electron meets with a hole, they recombine and these free carriers effectively vanish. The energy released can be either thermal, heating up the semiconductor (thermal recombination, one of the sources of waste heat in semiconductors), or released as photons (optical recombination, used in LEDs and semiconductor lasers). The recombination means an electron which has been excited from the valence band to the conduction band falls back to the empty state in the valence band, known as the holes. The holes are the empty state created in the valence band when an electron gets excited after getting some energy to overpass the energy gap.
The more abundant charge carriers are called majority carriers, which are primarily responsible for current transport in a piece of semiconductor. In n-type semiconductors they are electrons, while in p-type semiconductors they are holes. The less abundant charge carriers are called minority carriers; in n-type semiconductors they are holes, while in p-type semiconductors they are electrons.
In an intrinsic semiconductor, which does not contain any impurity, the concentrations of both types of carriers are ideally equal. If an intrinsic semiconductor is doped with a donor impurity then the majority carriers are electrons; if the semiconductor is doped with an acceptor impurity then the majority carriers are holes.
Minority carriers play an important role in bipolar transistors and solar cells. Their role in field-effect transistors (FETs) is a bit more complex: for example, a MOSFET has both p-type and n-type regions. The transistor action involves the majority carriers of the source and drain regions, but these carriers traverse the body of the opposite type, where they are minority carriers. However, the traversing carriers hugely outnumber their opposite type in the transfer region (in fact, the opposite type carriers are removed by an applied electric field that creates an inversion layer), so conventionally the source and drain designation for the carriers is adopted, and FETs are called "majority carrier" devices.
Free carrier concentration is the concentration of free carriers in a doped semiconductor. It is similar to the carrier concentration in a metal and for the purposes of calculating currents or drift velocities can be used in the same way. Free carriers are electrons (or holes) which have been introduced directly into the conduction band (or valence band) by doping and are not promoted thermally. For this reason electrons (holes) will not act as double carriers by leaving behind holes (electrons) in the other band. In other words, charge carriers are particles/electrons that are free to move (carry the charge). They get charged at the battery/cell, and then flow throughout the circuit, giving energy to any components in the way, then when out of charge and towards the end of the circuit, they get re-charged by the battery/cell.