Excellent and topical question…
The theory that describes the particles and forces that make up the Universe and how they interact is called the standard model.
There are particles with no mass – photons, which are the particles of light
There are particles with mass – electrons, nuetrinos, quarks, with quarks coming together to make up protons, neutrons and other exotic particles.
There are then particles called Bosons (After S Bose who described the general properties of such particles) which carry the different forces. So the photon is the electromagnetic interaction (how positive and negative charges attract), the W and Z carry the weak interaction (for radioactive decay) and the gluons carry the Strong force.
The Higgs is a Boson, so it mediates some interaction.
The question the Higgs deals with is Why do Particles Have Mass? This is in fact a very deep and subtle puzzle, as the ideal scenario is in fact that everything is a photon, with no mass, so mass must be introduced through some mechanism.
What Higgs and others said in the 1960s was the imagine you have an interaction in space (called a field) that essentially when it interacts with a particle endows it (somehow, still unknown) with mass. As I said, this is tricky stuff! An analogy is with the electromagnetic field, that is charges.The electron has a negative charge which arises when the particle interacts with the electromagnetic field, that endows it with this charge. When two electrons interact, they send photons between each other that repel the two negative charges.
Hope this helps – this is far a from trivial topic
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