Now, more skilled scientific minds than mine have debunked these doomsayers, but the stories are out there, and kids are bound to hear them. They're bound to have questions, including wanting to know what a hadron is, why scientists want to smash them together, and, by the way, are these European scientists about to suck the world into a black hole? Well, if they've taken high school chemistry, they've probably learned about protons and neutrons, so you can explain that both of those are in fact types of hadrons. You probably don't want to get into their valence quarks, unless you really understand quantum physics and don't mind your kids tuning you out. As for why they're doing it, it boils down to the search for the Higgs boson, also called the "God Particle," which is the only elementary particle that has never been observed by science. If your kids ask why that's so important, point out that it was nuclear research that led to the creation of the Internet, and they may just finally understand why science is so important! If they're also interested in how the LHC works, point them to this explanation on HowStuffWorks.
Now, the other question is a bit tougher, because you (I assume) don't want to outright lie to your kids, but you don't want to alarm them, either. It is actually possible, as I understand it, that the experiment will create subatomic black holes that will last a tiny fraction of a second before collapsing. But the likelihood of these black holes becoming the more well-known kind of black hole is nearly nonexistent.
That being said, if you've raised your kids in the proper GeekDad fashion, they'll have read a lot of science fiction by the time they hit high school. And sci-fi is, of course, full of stories about scientists with good intentions going too far and causing horrible consequences. So it's entirely understandable if your kids are a bit concerned about what's going on on the border between Switzerland and France.
My advice? Just tell them that there's really no chance at all that the world will end in the wee hours of the morning tomorrow. Seriously, how many times can you tell your kids something about the future without even the slightest worry you'll be proved wrong? If you tell them that and you're wrong, I guarantee your kids will never confront you about it.
OK, that may not have been as reassuring as I'd intended. Sorry about that. Seriously, unless every preeminent physicist in the world is very wrong, the LHC is perfectly safe. That's good enough for me.
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