The C of CP stands for charge conjugation, the P for parity. Charge conjugation is swapping a particle for an antiparticle, and parity is like looking in the mirror. If CP were not violated, then a particle interaction would look indistinguishable from an antiparticle interaction seen in the mirror. Moreover, all the matter and the antimatter which are believed to have been created in equal amounts at the Big Bang would have been annihilated by now and we would not be here to think about it. But thankfully, that has not happened.
Nature does indeed seem to have a preference, but it is a very subtle one.
Just one proton surviving for every billion protons and antiprotons produced at the Big Bang would be enough to make the Universe. Up to now, there is only one piece of experimental evidence for CP violation. In 1964, a subtle difference was measured at the Brookhaven laboratory in the United States between the decays of particles called neutral kaons and their antiparticles. LHC needs no explanation, and b refers to b quarks. Cross it out and your left with CP violation, just what LHCb will be measuring.