All elementary particles with half-integer spin () are called fermions because they obey Fermi-Dirac statistics - namely, no two identical fermions can be in exactly the same quantum state. (This rule includes the Pauli exclusion principle, but it carries over into many other branches of physics.) Examples of fermions are electrons, protons, neutrons, muons, quarks, ....
The name fermion honours Enrico Fermi, who (with Paul A.M. Dirac) described the special properties of this type of particles.