This discovery implies that the speed of light is not the basis for maximum velocity. Einstein's summary for time dilation in his relativity theories has its roots in the speed of light. A simple explanation would be to consider two observers with clocks in a single dimension without any gravitation forces acting on the system. Observer 1 is travelling at a much greater speed than observer 2. From the relative perspective of observer 2, obverver 1's clock will seem to be slowing down. According to the equation for time dilation, as observer 1 reaches the speed of light, his clock will appear to be stopped according to observer 2. In this sense, time does not exist for observer 1 in the relative frame of observer 2.
Now considering the new findings that there are particles that travel faster than the speed of light, that would then imply that these same particles are travelling in the negative time frame. That in itself is hard to believe. From what we think we know, this cannot be true, and thus the speed of light is no longer the basis for a large nuraber of physics theories. One being Einstein's E=mc^2 theory. Previously we had believed that the maximum amount of energy was created by a photon travelling at the speed of light. If these recent findings are true, then these neutrinos possess a greater energy threshold than the photon. In essence, a lot of the generalizations from the past 100+ years will be invalidated (not necessarily completely wrong, just not right). Finally, this brings up the question, if the neutrino posses a faster speed than the photon, what other particles possess an even faster speed that we have not discovered?