In February 2016 the LIGO team announced that they had detected gravitational waves on 14 September 2015. As far as I know, we already knew that gravity propagates at the speed of light. So two black holes orbiting each other and about to merge would produce the results observed. I don't see how that tells us anything new about the nature of gravity, or maybe I'm missing the point of the experiment. What did we actually learn from this experiment?
As far as I know, we already knew that gravity propagates at the speed of light.
The mathematical model of General Relativity has in its structure the velocity of light for gravitational waves. A model has to be validated and it is validated by observations and data. We did not "know", we had a hypothesis within a standard GR model.
So two black holes orbiting each other and about to merge would produce the results observed.
Black holes are also a mathematical model . There are observational data which are in agreement with the existence of black holes, but not definitive.
With the LIGO experiment the signal is mathematically consistent with gravitational waves and the behavior of two black holes within the General Relativity model. Thus GR as an underlying mathematical model of the universe has been validated by this observation.
What we have learned from the LIGO experiment is that gravitational waves exist as predicted by the general relativity model.
What did we learn by detecting a gravitational wave?
We learned that LIGO works.
When making a new scientific instrument, there's always the chance that some unforeseen problems will make that instrument work poorer than expected. For example, the fuzzy images first sent back by Hubble, the supposedly faster-than-light neutrinos; the list of scientific instruments that did not work according to expectations goes on and on.
Suppose it hadn't worked, that it ran for months and then years without seeing anything but noise. This is exactly what happened with the initial version of LIGO, which ran from 2002 to 2010 without seeing a thing. Nobody took those initial negative results as disproving general relativity. They instead took it as a sign that they needed to improve sensitivity, and by a good amount. Suppose that the improved LIGO hadn't worked. This, too, would not have been taken as a sign that general relativity was wrong. It would instead have been taken as a sign that LIGO was yet another scientific instrument that didn't pan out.
That's not what happened this time around. It worked, and it yielded a positive result much quicker than expected. The concept is now known to be sound. What we have learned is that there's much more to be done. More detectors around the world would be nice. Further improvements to sensitivity and directionality would be very nice. A set of gravitational standard candles would be very, very nice.
There's a solid wall, the surface of last scattering, beyond which even the best telescopes based on electromagnetic phenomena cannot see. Something else is needed to see beyond that surface. Perhaps neutrino detectors, but detecting high energy neutrinos is very hard. Detecting massively redshifted neutrinos is far, far beyond the capabilities of current science. The only other option (so far) is gravitation.
Now that we know LIGO works, LIGO (or something like it) is the best bet to being able to see beyond the surface of last scattering. And then we will learn something truly new.