As particles collide at higher and higher energies, different physical effects occur. For example, if atoms collide with high enough energies, they knock electrons off each other - they ionise. Experiments which map the cosmic microwave background (like COBE, WMAP and Planck) look at the physics from the moment (about 400,000 years after the start) when the universe got so cool that this ionisation stopped happening. Before that everything was plasma. Plasma is the stuff which glows in fluorescent lightbulbs.
Go further back, a few minutes after the big bang, and energies get so high that even atomic nuclei can't hold together. At this point, protons and neutrons are everywhere. These are the kind of energies you need for nuclear fusion, as is being attempted at ITER.
Back a big step further (about 0.00000000001 seconds after the big bang) and the protons and neutrons can't even stay whole. The quarks and gluons that they are made of spread over the whole universe (which is quite small at this point). This is a new form of matter we refer to as "quark-gluon plasma", though evidence from experiments at RHIC indicates it may behave more like a quark-gluon liquid in fact. This is the stuff the LHC will be able to reproduce now, and which the experiments will study - especially ALICE, which is built for this purpose.
This is a good explanation if you don't understand why, for example, RHIC and CEBAF are a bit different than LHC (when it was doing p-p collision) and the Tevatron, even though all 4 of them are basically particle colliders. They are studying different energy regimes, and possibly different types of processes.