Bosons are quantum particles that have integer spin. A classic example of bosons are photons because they have spin 1. Fermions are quantum particles that have half integer spin. A classic example of fermions are the electrons which have spin +/-(1/2) . Because of this bosons and fermions obey different statics in what it concern mainly their energies. Fermions obey the Pauli exclusion principle which forbids more than two opposing spin fermions to be on the same energy level. In contrast, bosons do not need separate energy levels to exists. they can occupy all the same energy level. In 1925, for the first time, starting from some observations that Bose made by calculating the statistics of bosons energies and predicted for the first time that boson particles could condense all in the lower energy state allowed occupying thus all a single energy level. This state was named the Bose-Einstein condensate. Experimentally this sate was observed in liquid Helium (liquefaction temperature 4.2 K) below a so named critical temperature of about 2.17 K. Helium atoms are bosons. In this state of Helium (below 2.17 K) a Bose-Einstein condensate forms and quantum effects are observed at the larger scale of the entire gas. For example the liquid becomes super-fluid (it has no viscosity) and the heat capacity has a big gap.
There has been made a parallel between the super-fluidity of liquid Helium and the superconductivity (which happens also below a certain critical temperature) of certain solids. In both cases a Bose-Einstein condensate forms, with the difference that the bosons that make the condensate in superconductivity are made from weak coupled fermions.