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A boson is a particle which has a whole number spin ('spin' is a quality assigned to subatomic particles).
A photon is an example of a boson as it has a spin of 1.
Bosons are different from Fermions, which are particles that make up matter, because they obey Bose-Einstein statistics. (This means that you can put two of them in the same place at the same time).
"Gauge bosons" carry forces. There are three known gauge bosons which are fundamental particles. For example, the photon carries the electromagnetic force. The four gauge bosons are as follows: photons for electromagnetism, gluons for strong force, and W and Z bosons for weak force. Other theoretical gauge bosons are predicted, such as gravitons for gravity. The Higgs boson is another fundamental particle of a type called a scalar boson.
Paul Dirac named this class of particles "bosons" in honor of a famous scientist called Satyendra Nath Bose.