As always, more data is needed before an actual "discovery" can be claimed. The T2K data run was cut short because the major earthquake that devastated Japan also damage the experiment's muon neutrino source. But researchers expect to have the machine back online and taking more data by January 2012. With more data, the current 3-sigma signal should strengthen sufficiently to claim a solid discovery. MINOS will also continue collecting data until February 2012.
Physicists want to know more about neutrino oscillations, and their masses, because this provides a potential clue to why there is something in the universe, rather than nothing. Back when our universe was still in its infancy, matter and antimatter were colliding and annihilating each other out of existence constantly.
This process slowed down as our universe gradually cooled, but there should have been equal parts matter and antimatter. Instead, there were slightly more matter particles than antimatter, and that slight excess formed everything around us. Physicists think that neutrinos, with their teensy-tiny bits of mass, might have been the tipping point that tilted the scales to matter's favor.