Bosons are subatomic particles that possess integer spin (i.e., angular momentum in integer units.) and are governed by Bose-Einstein statistics. Bosons mediate interactions between fermions. Bosons include photons, mesons (Pions and kaons), and nuclei of even mass number ( helium-4, etc.). Bosons differ from fermions in that any number of bosons can occupy the same quantum state Atoms only exist in certain  "quantum states" which are defined by a set of integer-like properties.

In 1924, Satyendra Nath Bose (1894-1974) published a paper "Planck's Law and the Hypothesis of Light Quanta" which led Albert Einstein (1879-1955) to seek him out for collaboration in developing a theory regarding the gas like qualities of electromagnetic radiation. The result was the Bose-Einstein distribution equation which solves for the average number of bosons in a particular energy state. Bose used this formula to derive Planck's black-body, energy distribution equation.
number(bosons) = 1 / ( e^x  - 1)

Where e is the base of the natural logarithms, and x = y + energy divided by Boltzman's Constant * temperature.

The Fermi-Dirac distribution equation which is used to compute the average number of fermions in a particular energy state was developed in 1926 by the physicists Enrico Fermi and P.A.M. Dirac.
number(fermions) = 1 / ( e^x  + 1)

Where e is the base of the natural logarithms, and x = y + energy divided by Boltzman's Constant * temperature.

Note that the Fermi-Dirac distribution equation is very similar to the Bose-Einstein distribution equation.

At high temperatures and low concentrations, both of these distribution laws tend toward the classical particle distribution law.
number(particles) = A*e^x

In Fermi-Dirac and  Bose-Einstein statistics "y" is a function of temperature and particle concentration,.
In the classical particle distribution law "y" = 1.