RANDALL: The Higgs boson is a particle associated with the masses of elementary particles. Notice the careful phrasing. There are two common misconceptions about the Higgs boson that are important to know if you want to truly understand it.
First of all, the Higgs boson is associated only with elementary particle masses such as that of the electrons or particles called quarks inside protons and neutrons. Most of the mass of common matter is a result of the strong binding force in those protons and neutrons. It would exist even without the Higgs boson. But the mass of the most basic particles we know about — those building blocks of matter of which all ordinary stuff is made — can only be explained by something called the Higgs mechanism.
The Higgs mechanism is a result of something called a field that extends throughout space, even where no particles are present. This notion is probably most familiar to you from a magnetic field. You feel a force between a magnet and your refrigerator even when “nothing” is there. A field can fill “empty” space. The Higgs field extends throughout space. Elementary particles acquire their masses by interacting with this field. It is kind of like space is charged and particles get mass through their interactions with this charge.
Now, back to the Higgs boson. The Higgs boson is not directly responsible for mass. The Higgs field is. The boson is a particle that tells us our understanding of this mechanism is correct. It also is a big clue as to where that field came from in the first place. Its discovery tells us that what we expected to be true was indeed correct, and it gives us clues as to what else might underlie the Standard Model.