The answer will be that the Higgs boson is a sort of wave in the Higgs field. You could have the field without having any of the bosons around (in fact, it's hard to get them) but the field sets up the possibility of their existence.
Let me try to explain this with a story about something that's easier to picture.
Look at a warm piece of iron. There are little magnetic fluctuations throughout it, but no organized magnetic structure. When it cools down enough (below what's called its Curie temperature), the little electron magnets pick some accidental direction and mostly line up pointing the same way. Ideally, at zero temperature, they all line up as much as their quantum nature allows. At any rate, once they start to line up there's a systematic magnetic field which wasn't there before, in one direction. In the plane at right angles to that, there's no systematic field. That's like the Higgs field, something that forms from a more complicated field when the universe cools down. Just as one direction of magnetic field becomes different from the others, one "direction" of field in an abstract space, not ordinary directional space, becomes a special field, the Higgs.
You can picture the lined up magnetic field as a collection of magnetic field lines, like strings under tension. One of the things they can do is stretch a little to the side, like strings, with waves propagating along them, like sound down a string. These waves are called magnons. So the magnons are wiggles away from the ideal lined-up state. You can't get magnons until some sort of lined-up state is there to begin with. There are different types of magnons traveling along the field and at right angles to it.
The Higgs particle is a sort of wiggle in the more abstract space, a type of wiggle that can't be there until the Higgs field forms. There are other types, (called W and Z) in other abstract "directions", like magnons not along the field direction. Back in the day, before the Higgs field formed, all these W, Z, and Higgs effects were jumbled together in one sort of fluctuation, like all the little magnetic fluctuations in all directions in iron above its Curie temperature.
Mike W.
(published on 02/18/2013)