What is the Higgs boson and why it's important

^^ 5 - 1 page explanations of the Higgs Boson

In the standard model, the Higgs field is an SU(2) doublet, a complex spinor with four real components (or equivalently with two complex components), with a Standard Model U(1) charge of −1. It transforms as a spinor under SU(2). Under U(1) rotations, it gets multiplied by a phase; this mixes the real and imaginary part of the complex spinor into each other, so this is not the same as two complex spinors mixing under U(1) (which would have eight real components between them), but instead is the spinor representation of the group U(2). After symmetry breaking, three of the four degrees of freedom in the Higgs field mix with the W and Z bosons, while the one remaining degree of freedom becomes the Higgs boson – a new scalar particle.

That clear? No, it fucking isn't. And it just gets fucking worse after that.

I'd really like to be able to form some kind of picture in my head of how a Higgs Boson gives mass to other particles, but I just can't... and if I could it would probably be wrong.

I don't see how Higgs explains (or in any way addresses ) the gravitational and inertial mass equivalence - the elephant in the room. Any mass theory that doesn't notice it is just a non-starter.

What we do know - gravitational waves exists (and thus gravitron - the quantum wave packet). The inertial mass in such approach arises naturally just as manifestation of gravitational mass. What we don't know here is the exact machinery how gravitational force interacts with matter.

Higgs boson doesn't helps here. It doesn't shed any light on the details of gravitational interactions, and its explanation of mass must be compatible with what we know while it doesn't seem to even start to address it.