Any massive particle composed of three quarks is called a baryon. Protons and neutrons are examples of baryons, since they have three quarks. Mesons, on the other hand, are particles that are made up of only two quarks. Both mesons and baryons are considered parts of the subatomic class called hadrons, which means that they are particles that are capable of interacting with a strong force. The reason for this is because they are made up of quarks, and quarks are particles which allow for strong interaction.
A baryon is also a particle which has a spin of a half-integer. Particles which have that kind of spin are called fermions.
There are many other baryon particles other than the proton, like the lambda, the sigma and the delta, but these particles are unstable when isolated. The only isolated baryon which is not unstable is the proton. If the particles were to be isolated, they would eventually decay to a proton.
Any baryon particle always has a counterpart called an anti-baryon. The anti-baryon is composed of anti-quarks of the opposite value.
Matter can be called baryonic matter if it is composed of particles with three quarks. These include anything made of atoms, which means most of the matter on Earth can be baryonic matter.