Re: This is not making physics any easier
Neutrino oscillation has been known about for a fairly long time. It's a critical result for two reasons.
Firstly it means that the Sun hasn't gone out, which is a good thing for the long-term future of life on Earth. Fusion in the Sun's core produces electron neutrinos, in huge numbers. Based on the Sun's luminosity (ie how bright it is!) we can estimate what the rate of fusion in the core must be, or in fact what the rate must have been some time ago, as the energy from processes in the core takes a long time to get to the surface where we can measure it. Knowing the rate of fusion means we can predict the neutrino flux passing the Earth. From the 1960s it became possible to detect these solar neutrinos, and it became apparent there was a serious problem: there weren't enough, by a factor of 1/2 to 2/3.
There are two possible reasons for this (three if you include experimental error, but multiple experiments saw the same problem). The terrifying one is that fusion could be stopping in the Sun: because neutrinos escape from the core immediately they tell you the rate of fusion in the core now (or a few minutes ago, in fact), while the Sun's luminosity tells you the rate thousands of years ago. So if fusion had stopped, or dramatically decreased, this would explain the result. It would also mean that stellar models were terribly wrong and that life on Earth had no future as the Sun was going out. The other possible reason is neutrino oscillation: the Sun emits electron neutrinos, and we detect electron neutrinos. But if neutrinos oscillate between three flavours -- electron, muon and tau -- then, between being created in the Sun and us observing them, the oscillation would mean we see only about 1/3 of the neutrinos we naively expect to see, as 2/3 of them would have leaked away into muon or tau neutrinos, which we don't detect.
Well, there are other ways of estimating what is going on in the Sun's core, and they predicted that fusion has not stopped. A bunch of other experiments with neutrinos were also done, including some which showed neutrinos produced in the experiment, at known rates, changing flavour. So neutrino oscillation turns out to be the right explanation, and the Sun has not gone out. The 2015 Nobel prize for physics was awarded for this work.
Secondly it means that neutrinos have mass. This is a lovely result because it comes straight from relativity. Massless objects travel at the speed of light, and thus along 'null curves', which are the curves (straight lines in the absence of gravity, curves in its presence) which light follows. But these curves have zero proper length, which means that objects following them experience no time: for a photon, or any other massless particle, everything happens at once. But this means that if neutrinos are massless then they can't oscillate, because they have no time to oscillate as everything happens at once for them: they experience no time between production in the Sun and detection in Earth.
But they do oscillate, and thus they must have mass. That's a lovely result because it follows so immediately from basic physics, but also because the standard model of particle physics -- the bits of theory we think we understand well -- predicts that neutrinos are massless. That means that the standard model is wrong and there is new physics we don't understand, and physicists (conspiratards notwithstanding) love that.