What determines the size of objects that we see around us or indeed even the size of ourselves? The answer is the size of the molecules and in turn the atoms that compose these molecules. But what determines the size of the atoms themselves? Quantum theory and atomic physics provide an answer. The size of the atom is determined by the paths of the electrons orbiting the nucleus. The size of those orbits, however, is determined by the mass of the electron. Were the electron's mass smaller, the orbits (and hence all atoms) would be smaller, and consequently everything we see would be smaller. So understanding the mass of the electron is essential to understanding the size and dimensions of everything around us.
It might be hard to understand the origin of one quantity, that quantity being the mass of the electron. Fortunately nature has given us more than one elementary particle and they come with a wide variety of masses. The lightest particle is the electron and the heaviest particle is believed to be the particle called the top quark, which weighs at least 200,000 times as much as an electron. With this variety of particles and masses we should have a clue to the individual masses of the particles.
Unfortunately if you try and write down a theory of particles and their interactions then the simplest version requires all the masses of the particles to be zero. So on one hand we have a whole variety of masses and on the other a theory in which all masses should be zero. Such conundrums provide the excitement and the challenges of science.
There is, however, one very clever and very elegant solution to this problem, a solution first proposed by Peter Higgs. He proposed that the whole of space is permeated by a field, similar in some ways to the electromagnetic field. As particles move through space they travel through this field, and if they interact with it they acquire what appears to be mass. This is similar to the action of viscous forces felt by particles moving through any thick liquid. the larger the interaction of the particles with the field, the more mass they appear to have. Thus the existence of this field is essential in Higg's hypothesis for the production of the mass of particles.
We know from quantum theory that fields have particles associated with them, the particle for the electromagnetic field being the photon. So there must be a particle associated with the Higg's field, and this is the Higgs boson. Finding the Higgs boson is thus the key to discovering whether the Higgs field does exist and whether our best hypothesis for the origin of mass is indeed correct.