The hope is that when these particles collide, the result will give evidence of the Higgs boson, and possibly other novel particles such as strangelets, micro black holes, magnetic monopoles and supersymmetric particles.
If you are wondering what use all this is, do bear in mind that some years ago, the team needed a way of sending stuff around to different universities, regardless of what operating system people were using. So they just invented the world wide web over coffee one morning. That is a slight exaggeration but only slight. The World Wide Web is a spin-off from this work.
We do not know what practical benefits will flow from this research. Thank God pure research can still be done and especially thank God that it is not governed by the pragmatic concerns of the English. Actually, we don't always get the pragmatism right, either. As Charles Babbage, the far-sighted inventor of the Difference Engine, a 19th century forerunner of the computer once said:
Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.(Physicists of the world - apologies if I have got anything wrong in the above. It is a while since I did Physics A-level.)
PS - I did get some things wrong. See ALICE in jeopardy.