It means that Einstein’s relativity — a theory of uncommon beauty upon which all of physics has been built for 100 years — is wrong. Not just inaccurate. Not just flawed. But deeply, fundamentally, indescribably wrong. It means that the “standard model” of subatomic particles that stands at the center of all modern physics is wrong. Nor does it stop there. This will not just overthrow physics. Astronomy and cosmology measure time and distance in the universe on the assumption of light speed as the cosmic limit. Their foundations will shake as well.
That's OK though. Science can get it wrong. It doesn't have to be right 100% of the time, even if it changes everything. What really matters is that we all get to do what we want to do. And whatever science we need in order to back that proposition we can keep thinking at least until we find a new one that will work. What really matters is that we get what we want.
Science gets it wrong. God doesn't ever get it wrong.