Many experiments have looked for particles traveling faster than light speed in the past and have come up empty-handed. Most troubling for OPERA is a separate analysis of a pulse of neutrinos from a nearby supernova known as 1987a. If the speeds seen by OPERA were achievable by all neutrinos, then the pulse from the supernova would have shown up years earlier than the exploding star's flash of light; instead, they arrived within hours of each other.So the result may be wrong. If it is correct, then there is something wrong with Einstein's theory of special relativity. If there is something wrong with special relativity, there is a big hole in all of our physics, because special relativity is, in our models, the bookkeeping by which the universe make sure that effects follow causes, and that the laws of science are the same for everyone. If it does not hold, there may be ways in which those laws can be very different for some observers in some situations -- a very big can of worms.
A lot of the secondary news about this story focused on time travel. This is because in Einstein's model, the closer you are traveling to the speed of light, the slower time passes for you. If you could travel exactly the speed of light, the equations imply, time for you would be frozen. Some people think this means that if you traveled faster than light, you would be traveling backward in time.
But this is, as my wife says, "just math." At the speed of light the equations break down and generate zero or infinite results, so one shouldn't place too much confidence in them. And the whole business of particles traveling back in time is a purely mathematical construct. If you graph the relationship between a particle's speed and the passage of time, it approaches closer and closer to an axial line representing the speed of light. (Imagine the old x/y plane from high school algebra.) Mathematically, this curve also has a negative version on the other side of the axis, and this mirror image might (might) represent particles traveling faster than light. But since nobody has, until now (maybe), seen a particle traveling faster than light, it would be dangerous to assume that they obey laws we understand. Remember that the backward in time business is not Einstein's own interpretation of special relativity; he thought special relativity made faster than light travel impossible. So any predictions special relativity makes about things traveling faster than light should not be taken too seriously.
And yet one more caveat: neutrinos are weird little things that interact very weakly with other matter -- trillions of them pass through your body every second -- so even if they can sometimes travel faster than light, other kinds of matter (like us) still may not be able to.