The Higgs boson gives elementary particles their mass, but 98% of the visible mass in the Universe (not dark matter) comes from a less famous mechanism: chiral symmetry breaking. This is why protons and neutrons are so much heavier than their quarks!

Briefly, protons and neutrons act like bags full of a soup of virtual quark-antiquark pairs, which give them most of their mass. This soup, called a 'quark condensate', breaks a certain symmetry that exists outside the bag: 'chiral symmetry', where you change the phase of the clockwise and counterclockwise rotating quarks separately. In the quark condensate, the clockwise spinning virtual quarks are entangled with counterclockwise spinning virtual antiquarks.

https://en.wikipedia.org/wiki/Chiral_symmetry_breaking

Chiral symmetry breaking - Wikipedia

@johncarlosbaez I know this is google-able, but I want to ask someone who knows more than me- what about bonding energy? I thought bonding energy accounted for a large amount of mass.

@cpkimber - if something has binding energy, it has *less* energy and thus *less* mass than it would otherwise have, because binding energy is the energy it would take to pull it apart. For example, when a hydrogen bomb goes off, the hydrogen nuclei fuse into something that has less energy and thus less mass, releasing a lot energy in the process.

https://en.wikipedia.org/wiki/Binding_energy

Binding energy - Wikipedia

@johncarlosbaez I knew that some time ago, but now feel like a kid for asking.
@cpkimber - no prob! I love questions about physics, and that was a good question.