When you smash a punch of particles together sometimes produce two quark particles that include bottom quarks called B mesons that in turn decay to produce two muons (heavy electrons). Sometimes they will be negatively charged, just like electrons. Sometimes they will be positively charged, just like positrons. Other things produced in these collisions, like kaons (another kind of two quark particle) also produce two muon decays.
The Standard Model predicts that negatively charged muons should outnumber positively charged muons due to known CP violations in the weak force by a factor of just 0.01%. The data from the almost full run of the D0 Tevatron experiment show a 0.787% excess of negative muons with an standard deviation of error of about 0.2%, implying a deviation of about four sigma from the Standard Model expectation. Thus, experiment implies that the 95% confidence interval is that there are something like 29 to 119 times too many excess negatively charged muons.
Further analysis of the data reveals that B-meson decay, rather than other possible decay pathways, seem to be behind the anomalous results.
Of course, in this case, like so much of the high energy physcis field, a deviation of less than 1% from the predicted value in a calculation that has lots of steps that depend on QCD calculations, imperfectly known experimental estimates for quantum physics equation constants, and what have you could easily arise from very subtle issues involved in generating the theoretically expected value of either the end result or the "background" that is subtracted out from the total result for processes we understand to get the part of the result attributable to the interesting part.
The four standard deviations of variance from the expected result only considers differences from the theoretical prediction that arise from fundamental quantum randomness. The error estimate in the result likewise considers only known levels of uncertainty in the inputs to the theoretical calculations and the current experimental process, not analytical errors or systemic problems with the laboratory setup that no one had considered when doing the calculations.
But, excess CP violations in heavy meson weak force decays in excess of those predicted by the Standard Model are something that we've observed repeatedly before (that's the main reason physicists knew to put any CP violations into the Standard Model at all), and by five sigma, observed effects tend not to vanish when efforts are made to replicate the effect, so there is good reason to believe that this is the real deal, the holy grail of HEP: New Physics!
Now, there are more theories out there to explain where this excess CP violation could come from than there are different kinds of hats in a Georgia church on a Sunday in June. But, for the most part, you can't fit the Standard Model to the data simply by tweaking the values of a few constants in the CKM matrix. Most of the proposals involve new particles that require a deep conceptual break with the structure of the Standard Models chart of fermions and bosons. It is the moral equivalent of trying to put together some assembly required furniture with a ordinary screwdriver and hex wrench only to discover as you try to assemble the final critical joint to complete the job that you also need a three foot long magnetized titanium corkscrew to connect parts you hadn't previously noticed were even in the box.
For my druthers, the most attractive extension of the Standard Model that could resolve the conflict between experiment and theory, because it is the least radical in its implications, is the possiblity that there are four rather than three generations of quarks and leptons, such as in this proposed Standard Model extension. A model with at least four generations of fermions could also explain data pointing to the possibility that there are more than three kinds of neutrinos. It also would make it possible to unify the gauge couplings without supersymmetry.