As to why many theorists are excited over news of a possible light Higgs boson with 125 GeV mass, here's a memorable excerpt from a September 2011 interview with Clerk Maxwell Professor of Theoretical Physics and former CERN staff member John Ellis:
In the first scenario (114-135 GeV), we could be looking at a Standard Model Higgs boson. This range has been refined experimentally: recent LHC results presented in Mumbai excluded the Standard Model Higgs from about 135 GeV to about 500 GeV, while LEP had previously excluded it up to 114GeV. That leaves a narrow low-mass range of about 20 GeV where it could lie. But if found in this range, the Standard Model theory would still be incomplete; the present electroweak vacuum would be unstable for such a light Higgs in the Standard Model, so we would have to come up with new physics to stabilise it.