Fermions are the class of particles that make up matter, including electrons, quarks, and protons. They are defined by having half integer spin, and by obeying a strict rule called the Pauli exclusion principle, which says no two identical fermions can occupy the same quantum state at the same time.
That single rule has enormous consequences. It is the reason electrons stack into distinct shells around an atom’s nucleus rather than all collapsing into the lowest energy level, which is why the periodic table has the structure it does and why chemistry works the way it works.
Fermions stand in contrast to bosons, the other broad category of particles, which include force carriers like the photon and can pile into the same state without any restriction. That distinction between fermions and bosons is one of the deepest divides in particle physics.
The exclusion rule that defines fermions is also what keeps matter from collapsing in on itself. Squeeze ordinary matter hard enough and its electrons resist being crammed into the same states, a resistance called degeneracy pressure that holds up white dwarf stars against their own gravity. Push even harder, past what electron degeneracy pressure can support, and the same principle shows up again with neutrons instead, holding up the far denser cores of neutron stars. Without this fermion-specific rule, there would be nothing physically stopping every particle in an object from settling into the exact same lowest-energy state, which means solid matter as we experience it, with its size, shape, and resistance to being crushed, simply would not exist.
Fermions also come in three generations of increasing mass, mirrored across both quarks and leptons, a repeating pattern that the Standard Model describes precisely but does not explain. Everyday matter is built almost entirely from the lightest, first generation fermions, since the heavier copies decay away in fractions of a second and only appear briefly in particle collisions or cosmic ray showers.