Let me explain to you what the Higgs boson is.
Just kidding! Nobody can explain to you what the Higgs boson is, because if they try they'll say things like: The Higgs boson is the particle that imparts mass to the other particles. And if you're thinking clearly you'll say: Wait, what does that mean? You mean if the Higgs boson disappeared, then the other particles would exist but wouldn't have mass? So how could they be particles at all--I mean, how could they be particles in the sense that I think of "particles"?
The answer to that question, I think, is that particles aren't really particles in the sense that you and I think of particles. At least, that would explain why physicists sometimes use "particle" interchangeably with "field." (And as for what a "field" is: It's like a particle, except different.)
Here , for example, from a BBC article that a few months ago tried to tackle this Higgs boson thing:
As the Universe cooled after the Big Bang, an invisible force known as the Higgs field formed together with its associated boson particle.
It is this field (and not the boson) that imparts mass to the fundamental particles that make up atoms.
I don't exactly know what it means for a field to be "associated" with a particle, but I do think that the word "field," for the layperson, is better for Higgs-related pedagogical purposes than the word "particle," because it plugs more easily into the common metaphor that the Higgs is like "molasses" that, by resisting the movement of all those non-Higgs particles, gives them mass. After all, a "field," in the layperson's vague sense of that term, is some sort of continuous expanse, and so is molasses. Kind of.
Actually, though, that same BBC article, even while promoting the Higgs field at the expense of the Higgs particle, trotted out a metaphor that tried to convey how a bunch of particles could be like molasses:
The way the Higgs field works has been likened to the way photographers and reporters congregate around a celebrity. The cluster of people are strongly attracted to the celebrity and create resistance to his or her movement across a room. In other words, they give the celebrity "mass".
In sum: I personally continue to have no idea what the Higgs boson is. And I think the physicists who 'understand' what it is can do so only because they don't have the layperson's compulsion to think about the world in ways that are ultimately metaphorical. Or, at least, these physicists have dropped the idea that to truly understand something is to have a crystal-clear metaphor in your mind, a metaphor that doesn't break down at any point and doesn't contain internal contradictions. For them, apprehending a purely mathematical description of something is tantamount to comprehending it.
For the rest of us, I suspect, the Higgs belongs in the same category as various other parts of modern physics: It is yet more evidence that the human mind, to the extent that it was designed by natural selection to truly comprehend anything at all, was designed to comprehend the macroscopic world, not the microscopic world.
So, as for the question of what this Higgs boson thing ultimately "means": It means we should all try to have some intellectual humility, especially when opining on grand philosophical matters, because the thing we're using to try to understand the world--the human brain--is, in the grand scheme of things, a pretty crude instrument. Or, I should say: That's what I think the Higgs Boson means.