One, it is yet another validation of Einstein, and every new confirmation increases our confidence in his original theory. Of course, if no gravity waves had been observed, that would not have disproved General Relativity, it could have just meant our experiment was not working properly. Or to put it another way..."you can't prove a negative".

Two, this discovery gives us another tool to probe the early universe. Gravity waves can theoretically be detected from all the way back to the Big Bang itself. (Although we certainly don't have the technology to actually do that now.) Still, now we have the means of doing so, in principle.

Our only other means of studying the early universe is by detecting electromagnetic radiation. Light and radio from telescopes. Unfortunately there is a wall in time beyond which we cannot see. Right after the universe was created at the Big Bang, all the matter in the universe was a hot, extremely dense plasma opaque to light. After a few hundred thousand years, this ball of fire had expanded to the point where temperature and pressure dropped and electrons found atomic nuclei, and the plasma became electrically neutral--and transparent to light. The universe flashed, like an enormous flashbulb, and an explosion of light flooded the cosmos--yeah, "let there be light".

We can still see this flash today, bouncing around the universe, from every direction, it has been redshifted down to the 3 degree blackbody radiation we call the "microwave background". This faint radio radiation is our proof the Big Bang happened, and it was first observed in the 1960s although it had been predicted as far back as the 1930s. It is the earliest evidence we have of the early universe, but it only goes back to the time when the early universe was still opaque to light. We can't see back any further because that was before space became transparent (hot plasmas are opaque to electromagnetic radiation, neutral gas is transparent).

But now we have a method to retrieve information from beyond that horizon, because gravity waves can travel through an opaque plasma. In theory, we should now be able to observe what happened all the way back to the very moment of the Big Bang itself. It won't be like watching a movie, it will probably be just a signature, a waveform on graph paper. But it will give us hints as to what conditions were like back then, just like the microwave background has about the Big Flash.

Our studies of the microwave background have already told us a lot about the early universe, as I hinted above. For example, we know the background is very smooth, but not perfectly so, it seems to have tiny, barely-detectable wrinkles in it, and these flaws are probably the imperfections which led to the creation of the largest known structures in the universe, the filaments and voids made up of superclusters of galaxies.

This particular observation isn't from the early universe, it seems to have been generated by a black hole collision about a billion years after the Big Bang. But at least we know now that it is possible to receive information from before the Big Flash. These are indeed exciting times.