Journeying into unknown territory in physics is not exactly like Jason and the Argonauts sailing in unknown waters.
If you set up a normal experiment, I can tell you with good accuracy what will happen, or at least the probability of each outcome. For example, if you drop a ball from height h then I can tell you that it will fall towards the ground at such a speed, with such an acceleration and will take a certain amount of time to get there, and I'll be accurate to within 0.0001% or so.
With the LHC, we are testing new laws of physics - trying to measure particles that only normally occur in the middle of stars, at great temperature and pressure. We've no prior info for what these particles will do - we don't know how they behave when they hit something, we don't know if they can hit things - they may just sail straight through. There's lots of different theories, and the experimental results from the LHC will help us see which theory is closest.
Without your having had a decent background in physics (undergrad at the very least), it's difficult to explain exactly what we're doing. Basically, there's not really any danger - all that stuff about "sailing into unknown waters" and "it could destroy the world!!!" is because these machines are very expensive, and in order to justify the cost to the politicians who fund them, saying that there are innumerable benefits to society etc. is all very well, but saying that there's been lots of telly and newspaper coverage is what the politicians like best. And nothing sells TV programs and newspapers like "OMG!!!They're goin to end the world!!!!!11!one!".
You've more chance being blown up by a terrorist, much more chance of being killed by an STD and much, much more chance of being killed in a road traffic accident. Put it this way - if we all die because of CERN, I'll give you my kite stuff, and £100 on top