I find this stuff fascinating.
With this discovery, they're starting to talk about what happened before the big bang:
Video - Breaking News Videos from CNN.com
From my layman's understanding, it's not the particle itself that gives everything mass, it's the Higgs field. The field is like syrup. As other particles (protons, electrons, etc) travel through it, they get dragged down. Some particles don't interact with this field at all, they are the particles with no mass.
The particle itself is just a localized excitation of the field. In the LHC, the field got excited via the collisions they caused. The field is everywhere, even if there are no particles present.
The electro-magnetic field is similar. It's everywhere. A localized excitation of the field is a photon, but the field is everywhere.
I think of a photon traveling through the EM field like a ripple travels through water. The water remains motionless, yet the ripple travels.
Like I said, fascinating.