Fermions, in particle physics, are particles that obey Fermi-Dirac statistics. This is as opposed to bosons, which obey Bose-Einstein statistics. They generally have half odd integer spin. For example, 1/2, 3/2, etc...
The particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these. This includes all baryons and many atoms and nuclei.
Some fermions are elementary, such as electrons, while some are composite, such as the proton. According to the spin-statistics theorem, in relativistic quantum field theory, particles are either bosons (integer value spin) or fermions (half-integer spin.)
A consequence of the Pauli exclusion principle is that only 1 fermion can occupy a certain quantum state at a given time. Fermions are usually associated with matter. Bosons are generally force carriers. Weakly interacting fermions can also display bosonic behavior under extreme conditions.
Composite fermions, such as the proton and neutron, are the key building blocks of everyday matter.
The Standard Model of particle physics distinguishes two types of elementary fermions: quarks and leptons. In all, there are 24 total:
6 quarks: up, down, charm, strange, top and bottom
6 leptons: electron, electron neutrino, muon, muon neutrino, tau and tau neutrino.
The corresponding antiparticle counterparts to each of these.
Paul Dirac
Enrico Fermi
Paul Dirac was the one to name Fermions, after Enrico Fermi.