Baryons include both protons and neutrons, which are each formed from 3 quarks (held together by gluons, which provide the "strong force").
Hadrons are composite particles (i.e. particles that are made up of other particles). So baryons (protons and neutrons) are a type of hadron. Mesons are the other type of hadrons and are composed of a quark together with an anti-quark.