Fermions, named after Enrico Fermi, are particles with 1/2 integer spin; fermions are subject to the Pauli exclusion principle. All basic building blocks of matter are fermions; examples include electrons and quarks. Particles with integer spin, such a photons, are called bosons.
The fact that two fermions cannot occupy the same quantum energy state has important implications. It is the reason that you can build a sand castle out of protons, neutrons, and elections while you cannot build a sand castle out of light and gravity. Because there is nothing to prevent bosons from moving to the lowest energy state there is nothing from keeping your "light castle" from falling apart. By contrast, a fermion cannot move into a lower energy state if there is another fermion already there. So a grain of sand prevents another grain of sand from occupying the same location.