Bose-Einstein statistics (B-E statistics or the Bose-Einstein distribution) describes a distribution of the energy levels of non-interacting, indistinguishable particles if they are in thermodynamic equilibrium and are bosons, i.e., not bound by the Pauli exclusion principle.
The Pauli exclusion principle, which applies to some other types of particles (called fermions), is the fact that no more than one such particle within a quantum system will ever occupy the same quantum state. The analogous distribution of their energy levels is called Fermi-Dirac statistics or Fermi-Dirac distribution.
Bosons include photons and gluons and fermions include quarks, protons, and neutrons, but a composite particle with an even number of fermions (e.g., a helium nucleus of isotope 4) is a boson, and helium's superfluid state at sufficiently low temperatures is a result of B-E statistics.
If the temperature is sufficiently high and/or the particles are at a sufficiently low concentration, both Bose-Einsteins statistics and Fermi-Dirac statistics approach the classical formulation, Maxwell-Boltzmann statistics.