A baryon is a composite particle comprised of three quarks. Examples are protons and neutrons, which make up nearly all the mass of matter in the universe. Baryons, along with mesons, which are comprised of two quarks are hadrons (composite particles). Non-composite particles (elementary particles in their own right) include leptons such as electrons and neutrinos, and bosons such as photons.
The term baryonic matter (matter made of baryons), in effect is matter made of atoms, and the term non-baryonic matter (or nonbaryonic matter), obviously means made of something else. Neutrinos, and mesons, and free electrons would seem to fall under the category of non-baryonic matter, but the term is typically used to refer specifically to dark matter, under the assumption that dark matter is not made of atoms, e.g., made of WIMPs instead. Baryonic matter is typically used to mean "all the usual matter", i.e., other than dark matter.