I don't think I had a clue about hypervalence in high school. Actually I don't think I really have much of a clue about anything chemistry related when I was in high school.
I suppose I would have covered the octet rule. I would also have covered s,p,d, and f orbitals and explained that as we increase the shell from 1 to 2 to 3 and so on that the s,p,d, and f orbitals start to get closer and closer in energy (see diagram at the end of this webpage since my words probably aren't doing justice
http://www.chemguide.co.uk/atoms/properties/atomorbs.html).
Then I'd say something like "Once you get to shells of 3 or greater, the difference in energy between filled orbitals and the next shell's empty d orbitals starts to become smaller and smaller. In some compounds the energy difference is small enough that we can actually go ahead and fill those empty d orbitals with electrons. The end result is that we have more than the usual 8 electrons and thus it looks as if we have broken the octet rule." I know it's a lot more complicated than that, but for high school I think that's as far as I'd go without fear of completely losing everyone.