Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons.
In the Standard Model, there are three kinds of gauge bosons, corresponding to the electromagnetic, strong and weak forces. Photons are gauge bosons of the electromagnetic interaction, the weak interactions are mediated by weak bosons or "vector bosons", and the carriers of the strong interaction are known as gluons. Because of confinement, isolated gluons do not occur, at least at low energies and what we have are massive glueballs instead.
In a quantized gauge theory, gauge bosons are quanta of the gauge fields. Consequently, there are as many gauge bosons as there are generators of the gauge group. For example, the 8 generators of SU(3) correspond to 8 different varieties of gluons in quantum chromodynamics. Gauge bosons are described mathematically, for technical reasons such as gauge invariance, by field equations for massless particles. At a naive theoretical level therefore, all gauge bosons are required to massless, and the forces that they describe are required to be long-ranged. The conflict between this idea and experimental evidence regarding the short range of weak interactions required further theoretical insight, and is understood today in terms of the Higgs mechanism. This process also results in massive gauge bosons from hitherto massless particles. Photons and gluons are massless gauge bosons, whereas the W and Z bosons of electroweak theory have mass.
There is a fourth kind of gauge boson, the graviton, which has been postulated as the carrier of the gravitational force, but in the absence of experimental evidence, and a mathematically coherent theory of quantum gravity, this is a speculative matter at the moment.