In particle physics, a fermion is a type of particle that obeys the rules of Fermi-Dirac statistics, namely the Pauli Exclusion Principle. These fermions also have a quantum spin with contains a half-integer value, such as 1/2, -1/2, -3/2, and so on. (By comparison, there are other types of particles, called bosons, that have an integer spin, such as 0, 1, -1, -2, 2, etc.)
Fermions are sometimes called matter particles because they make up most of what we think of as physical matter in our world, including protons, neutrons, and electrons.