Bosons are particles which have integer spin 0,1,2.... They do not need to obey the Pauli exclusion principle, unlike fermions, so many bosons have have the same combination of quantum number in the same space. The wavefunction which describes a collection of bosons is symmetric with respect to the exchange of identical particles, while the wavefunction for a collection of fermions is antisymmetric. Bosins tend to have the lowest energy levels, while fermions are forced into higher energy levels by the exclusion principle.
Photons are bosons, which allows a light ray to contains many photons in identical states and makes lasers possible. All of the particles which carry the fundamental forces - gravity, the electric force, the weak force and the strong force - are bosons. These force carrying particles are known as exchange particles.