There is a nice article by Frank Close, Higgs boson: beginning of the end or end of the beginning.
It gives a succinct discussion of the background to the recent discovery and what it does and does not mean for elementary particle physics.
A couple of points I found helpful.
Reports in the media that "the Higgs boson is responsible for mass" are misleading.
First, almost all the mass in our bodies comes from neutrons and protons, and more than 99% of their mass comes from the binding energy of quarks (due to quantum chromodynamics) and not from the mass of isolated quarks.
The latter are hypothesized to get their mass from the Higgs field.
[Aside: the boson and the field are not the same thing. The boson is one specific excitation of the field].
Secondly, the CERN experiments do not establish that leptons and quarks obtain their mass from the Higgs field. Rather, only that the gauge bosons in electro-weak theory obtain their mass from the Higgs field.
Further experiments at CERN in the next few years may establish this though.
But, the existence of the Higgs field is relevant to chemistry in the following sense. Nuclei are so compact because of the large energy of pions, which is a reflection of the mass of quarks. Furthermore, the size of hydrogen atom is determined by the
mass of the electron.