MINOS is an experiment at Fermilab studying neutrino oscillations where one type of neutrino changes into another. Such changes were recognised some time ago as the explanation for missing neutrino fluxes from the sun and can only happen because the neutrinos have a small mass.
MINOS measures these oscillations and deduces a value for the differences between the squared masses of the different neutrino flavours. For the electron and muon neutrino the value they get is 2.35 x 10-3eV2.
Now they have also succeeded in getting a value for the same number using anti-neutrinos and the value is 3.35 x 10-3eV2 This means that for at least one of the neutrino flavours the mass must differ between the particle and its anti-particle. Differences between the interactions of particles and anti-particles are signatures of CP violation and have been well-studied for heavier particles, but this kind of mass difference would signal a much more surprising violation of CPT symmetry.
In relativistic quantum field theory and all other known generalisation of particle physics models, CPT must be conserved, even in string theories. If it is broken then physicists would have to invent a whole new way of building their theories.
Luckily the measurement comes with errors bars and the statistical significance of the result is only 2 sigmas which mean it could be a statistical fluctuation with a probability of 5%. In particle physics this level of certainty is not considered much to dance about. Given the very strong theoretical constraints against CPT violation we should expect this result to fade away as more data is collected.
However, the precision measurement of neutrino mass parameters is itself an outstanding achievement well worth knowing about.