Is the essence of the discovery of gravitational waves that we now know that gravity propagates through space at the speed of light and not instantly?
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Assuming you mean the direct detection of gravitational waves:
- it is another prediction of GR which has now been confirmed by experiment -- a test that GR has passed in other words;
- it is a direct detection of black holes interacting, which is, in fact, another test of GR it has passed;
- and finally it is an important step in a new kind of astronomy and an astonishing bit of engineering.
Although I am not an astrophysicist, I think that the masses of the two black holes were unusual, in terms of current models for their formation, so this particular event may also lead to changes in how we think about various astrophysical processes.