Point of scientific accuracy: the Higgs mechanism may explain why quarks and leptons have mass. Most of the mass of ordinary matter, however, comes from protons and neutrons, and they don't get their mass via the Higgs mechanism, but through quantum chromodynamics. (You can't just add up quark masses to get the proton and neutron masses).
Forgive a humble engineer for interrupting when physicists are speaking about the secrets of the universe, but something about your statement struck me as strange.
I am used to thinking about mass (gravitational or inertial) as being a fundamental property of things, not to be explained so much as described or measured. The concept of mass would seem to be more basic than the Higgs mechanism; how, then, can the Higgs mechanism explain why things have mass?