The io9 article Did they really detect the Higgs Boson? discusses this question and has links to even more details and background information.
As for why we should care, the article offers these two reasons:
This is a big deal because 1) The Higgs Boson is the last undetected particle in the Standard Model of physics, and 2) The Higgs field is what gives other particles their mass.
The author gives his opinion on whether or not the the Higgs Boson has really been found.
But particle physicists like to be more careful before they say something has been officially “discovered.” They normally demand a 5-sigma detection — with less than a one in a million chance of being wrong. It makes sense to set a high bar, but for my part, I’m convinced that the Higgs is real and that we know its approximate mass. The remaining work will be to make it official.