Hadrons, from Greek "hadros" for "robust", are particles that interact via the strong nuclear force i.e. the force between the "color charges" of their ingredients, namely quarks and gluons. Quarks and gluons themselves are not considered hadrons; hadrons are only the particles that may exist in isolation.
Hadrons may be divided to baryons and mesons (plus much more exotic classes); baryons are made of three quarks, mesons are made of a quark and an antiquark. The protons and neutrons are the most well-known and widespread examples of baryons (hadrons).
The relationship between hadrons and the Higgs boson is minimal, except that all of them are particles in particle physics. While hadrons are defined by their strong nuclear interactions, the Higgs boson is a key particle in a totally different force of Nature, the (electro)weak nuclear interaction. I guess it is a good idea to study the elementary particles a bit more systematically, rather than learn two words for particles and conjecture that they must be related. There are many particles in particle physics!
So the main relationship is that we discovered the Higgs boson by colliding hadrons – namely pairs of protons – at the Large Hadron Collider. But the reasons why protons are able to produce Higgs bosons at all are pretty complicated and that's partly the reason why it took so much time to artificially create Higgs bosons.