"We observe in our data clear signs of a new particle, at the level of 5 sigma, in the mass region around 126 GeV." This quote from Fabiola Gianotti of the ATLAS experiment, which worked with CERN for this research, captures the importance of this discovery. The 126 gigaelectron-volts is in the narrow range of energies the Higgs boson is expected to be at and 5 sigma means the likelihood of this result being an error is so remote, it can be considered a scientific fact.
The Higgs boson is one of the few remaining particles predicted by the Standard Model to be discovered. It is very important for it to be discovered to confirm the Standard Model as being an accurate way to describe the particles in the Universe and to explain how other particles have mass. The thinking is that there exists a Higgs field, which all matter interacts with, and these interactions cause a particle to have mass. If you disturb the Higgs field enough though, with high energy particle collisions for example, it should produce its bosons, similar to how disturbing an electromagnetic field will produce photons, another boson.
While the results released today are a big shot in the arm for those searching for the Higgs boson, the celebrations for the discovery may be misplaced in the end. Without a doubt, the researchers at CERN, ATLAS, and CMS have found a new particle, but these preliminary data do not tell us anything about its behavior. There is still a possibility some other previously undiscovered and unpredicted particle has been found. Only a great deal more analysis and new experiments will determine that.