The Higgs boson is a particle associated with the electroweak-symmetry breaking mechanism that was proposed in the 1960s and is a vital component of the Standard Model of particle physics. It is believed that all fundamental particles in the known Universe that have mass — for example electrons, or the quarks that live inside protons and neutrons — acquire this mass as a result of interacting with an omnipresent field through Higgs bosons. Massless particles, such as photons, pass through the field without interacting with it.
But why should you care?
Everything that we can touch and see and feel has substance. All this substance that makes up our Universe is courtesy of the familiar atom, which gives us all the matter around us. An atom is comprised of lightweight electrons orbiting and bound to a bulky nucleus of protons and neutrons, which themselves are made of quarks.
Our Universe with massless electrons
The electron is extremely light, with a mass just over 0.0000000000000000000000000009 grams (or about 0.51 MeV/c2). We believe that it gains this (albeit tiny) mass due to the fact that it is influenced by the Higgs field. Without this influence, our Universe would have a completely different structure.
In a simple hydrogen atom for example, the radius of the electron's orbit is inversely proportional to the electron’s mass. A massless electron would therefore be at infinity from the proton, not allowing atoms to form at all.
Protons, neutrons and the Higgs boson
In Nature, heavier particles tend to decay into lighter, more stables particles. Spontaneous radioactive β decay occurs when neutrons inside the nucleus are converted into protons, by the emission of a W− particle — a heavy particle that also gets its mass due to the Higgs field.
In addition, the up and down quarks, that combine to form protons (uud) as well as neutrons (udd), gain mass from their interaction with the Higgs field. However, their masses contribute only ~1% of the mass of protons and neutrons. The bulk of the mass comes from the energy holding the quarks together, which is greater for the proton than the neutron.
Without the Higgs field, quarks would have no mass and consequently the proton would be heavier than the neutron, since all their mass would come from their respective binding energies. Now, without the Higgs field, the W− particle would have a much smaller mass, protons would spontaneously and almost instantly decay into neutrons — we would have a Universe without protons.
Our familiar Universe with galaxies, supernovae, planets and life would not exist without mass, and our very existence is thanks to the all-pervading Higgs field.