As Brian Cox puts it, (Anyone who thinks the LHC will destroy the world is a Twat).
Brian Cox is the rockstar of physics, meaning he is the frontman for speaking and educating anyone who cares to hear what the LHC will do. He is one of the heads of the Atlas detector on the LHC, one of 4, which will detect the Higgs Boson(Refferred to now on as the "H") particle.
The Higgs Boson particle is the undiscovered, but much sought after particle that gives atoms their mass. So far, CERN and other colliders havent been able to detect it, but have detected results of the H particle. Hydrons will be spun around at 99.99996%(roughly) the speed of light, and collided in the detectors to help discover this particle.
Discovery of this particle will help greatly solve the "Grand unified theory", which links the theories of Graivty and Quantam Mechanics together, to solve how the universe works. It may also help to explain why gravitation is so weak compared to the other three forces. In addition to the Higgs boson, other theorized particles, models and states might be produced, and for some searches are planned, including supersymmetric (string) particles, compositeness (technicolor), extra dimensions, strangelets, micro black holes and magnetic monopoles.
The first run of sending a beam through the LHC at opperating temperature is September 10, 2008. But attempts at full force arent schedulled until 2009.
So, in short, it wont blow up the world, it will help unify theories and solve many problems plaguing physicists today, and IFF (If and only if) it does blow up the world, we have roughly a year until done so.
Hope that helped clear things up.