A baryon is a composite particle made of three quarks, such as a proton or neutron. They make up nearly all the mass of matter in the universe. Baryons, along with mesons, which comprise two quarks are hadrons.
Electrons and neutrinos are leptons, which are not made of quarks, but are elementary particles in their own right. Photons are examples of particles that are neither leptons or hadrons.
The term baryonic matter means matter made of baryons, in effect, matter made of atoms. Non-baryonic matter (or nonbaryonic matter), in turn, obviously means made of something else. This places neutrinos, and mesons, and free electrons 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.