I don't know, how to explain the inner workings of the Standard Model to high school students, because for this you need pretty advanced math on groups to describe symmetries and quantum field theory including renormalization of non-Abelian gauge symmetries.
The point is that quantum flavor dynamics (aka. Glashow-Salam-Weinberg model) is based on a local chiral gauge symmetry with gauge group \mathrm{SU}(2)_{\text{wiso}} \times \mathrm{U}(1)_{\text{Y}}. Where "wiso" stands for "weak isospin" and "Y" for hypercharge.
The "matter particles" involved are the leptons and quarks, that are grouped into three families. The model works with any number of families. For the first family the left handed parts of the lepton and quark fields build isospin doublets
\psi_{Le}=\begin{pmatrix}<br />
e \\ \nu_e \end{pmatrix}, <br />
\quad \psi_{Lq}=\begin{pmatrix}<br />
u \\d<br />
\end{pmatrix}.<br />
The right-handed parts are iso singulets. The very same structure is used for the other two families grouping together \mu,\nu_{\mu}; c,s (2nd generation) and \tau,\nu_{\tau}; t,b.
There are three gauge bosons for the isospin symmetry and one for hypercharge symmetry. For all these particles it is forbidden to write down naive mass terms, because this would break the local gauge invariance. That's immediately clear for the gauge fields, because this would involve mass terms \propto A_{\mu} A^{\mu}, which is not a gauge-invariant expression. For the leptons and quarks it's due to the chiral nature of the interaction. Since the gauge fields couple differently to the left and righthanded parts, there must not be any terms that mix these terms in a naive way.
To provide mass to the particles as observed, one must necessarily use the Higgs mechanism. In the minimal version (which seems to be the one realized in nature as is indicated by the newest results on the Higgs boson at the LHC) you introduce a isospin doublet of scalar-boson fields, but with a mass term of "the wrong sign". Together with a isospin symmetric four-boson coupling you apparently get spontaneous symmetry breaking, i.e., the scalar boson fields must have a non-vanishing vacuum expectation value, which can be chosen arbitrarily in any direction of the Higgs-field doublet (which are given by 2 complex, i.e., 4 real field-degrees of freedom). The gauge group is thus spontaneously broken to \mathrm{U}(1)_{\text{em}}.
Via the minimal couplings of the gauge bosons to the Higgs doublet the constant vacuum expectation value (vev) leads to a mass term for three of the four gauge fields, one of which turns out to be electrically neutral as it turns out when expressing the gauge fields in terms of their mass eigenstates, the Z boson, and the other two form the two charged W bosons. The remaining gauge field stays massless and is identified with the photon field.
Now, the leptons and quarks remain still massless, but that can be "cured" by writing down couplings between the leptons and quarks with the Higgs doublet, i.e., one forms an iso doublet with the left- and righthanded pieces and combines it in a gauge symmetric with the Higgs doublet. After the spontaneous symmetry breaking the leptons and quarks acquire a mass, but for the quarks the isospin eigenstates do not coincide with the mass eigenstates (as we know now, that also holds true for the leptons, because one has observed neutrino mixing which is only possible for massive neutrinos; in the here discussed original GSW model the neutrinos are kept massless and thus there's no mixing in this approximation).
The key observation of Anderson, Brout, Englert, Higgs, Kibble, Guralnik, and Hagen was that the spontaneous breakdown of a local gauge symmetry does not imply the existence of massless Nambu-Goldstone boson as is the case for the spontaneous breaking of a global symmetry.
The latter mechanism is at work in approximate form in the chiral symmetry in context with the strong interaction, where the quark-condensate vev is responsible for the spontaneous breaking of the approximate chiral symmetry in the light-quark sector. There the pions turn out to be the (pseudo-)Goldstone bosons of the breaking of this global symmetry.
For the case of a local gauge symmetry the "would-be Goldstone bosons" can be "gauged away", i.e., by the choice of a particular gauge, one can lump three of the four real Higgs-field degrees of freedom into the gauge boson fields. This is necessary, because a massless vector field has only two physical degrees of freedom (there are only two polarization states of the electromagnetic field, i.e., the massless photon) but a massive vector field has three physical spin-degrees of freedom. Thus in "absorbing" the would-be Goldstone modes into the gauge bosons they provide the necessary third physical spin component for these gauge bosons.
Since only three of the four Higgs-field degrees of freedom are absorbed in this socalled unitary gauge, first of all the fourth gauge boson remains massless (as it should be, because the photon is with an amazing precision found to be indeed massless). Second, and this was the unique contribution by Higgs, there must remain one scalar boson in the physical particle spectrum, which justifies the name "Higgs boson" for this physical particle and after all the Nobel prize to be given only to Englert and Higgs and not to the other people, who also published the idea of spontaneous breaking of a local non-Abelian gauge symmetry to provide mass to gauge bosons without explicit breaking of this gauge symmetry, which would spoil the entire consistency of the model making it useless as a physical model of elementary particles.
The real breakthrough of this model came when 't Hooft and Veltman could prove that non-abelian gauge theories (no matter if the gauge symmetry is spontaneously broken or not) is renormalizable as long as one only admits "superficially renormalizable" terms in the original Lagrangian. The key issue in the broken case is, not to choose the unitary gauge here, but another gauge, invented by 't Hooft and Veltman (the socalled R_{\xi} gauges). This leads to the usual power counting of diagrams and thus the renormalizability of this kind of gauge theories. Since the unitary gauge is a smooth limit of the R_{\xi}, the resulting S-matrix, which is gauge invariant, is renormalizable and unitary.
Last but not least one must mention that the Standard Model's gauge group is also free of anomalies, thanks to the specific charge pattern of the leptons and quarks. Here it is very important that this constraint matches with the -1/3 and 2/3 charges of the quarks and their additional color charge (each quarks comes in three colors). All together the Standard Model based on the here summarized quantum flavor dynamics and Quantum Chromodynamics for the strong interactions, builds a pretty beautiful model that in addition withstood all attempts to find deviations of the behavior of elementary particles, and this is true although the particle physicists would really like to find deviations from the Standard Model to solve some issues this model still has on the theoretical level, but that's another story.
For a somewhat more explicit explanation about this fascinating model, see my transparencies of lectures (see Lecture 1 for a brief review of the Standard Model), I've given recently to graduate students:
http://fias.uni-frankfurt.de/~hees/hqm-lectweek14/index.html
For a very clear exposition of the whole Standard Model, see
O. Nachtmann. Elementary Particle Physics - Concepts and Phenomenology. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1990.
As I already said above: I do not know, how you can translate this to high-school level. Perhaps the following popular physics books help:
L. Lederman, D. Teresi, The God Particle
and
F. Close, The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe
