In particle or quantum physics, fermions  are any particles characterized by Fermi–Dirac statistics and following the Pauli exclusion principle; fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei.

Fermions was a name coined by Paul Dirac from the surname of Enrico Fermi.

Fermions contrast with bosons which obey Bose–Einstein statistics.

They can be elementary or composite particles

Fermions can be an elementary particles, such as the electron; or it can be composite particles, such as the neutron or proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

Besides this spin characteristic fermions have another specific property: 

they possess conserved baryon or lepton quantum numbers.

 Therefore what is usually referred as the spin-statistics relation is in fact a spin-statistics-quantum number relation.

Quantum mechanical property

Only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. 

Fermions are usually associated with matter, whereas bosons are generally force carrier particles; although in the current state of particle physics the distinction between the two concepts is unclear.

Composite fermions, such as protons and neutrons, are key building blocks of everyday matter. 

Occasional exception

Weakly interacting fermions can also display bosonic behavior under extreme conditions, such as in superconductivity.

source: adapted from http://en.wikipedia.org/w/index.php?title=Fermion&oldid=609585580