Gravity is not "solved" by the discovery of gravitational waves. They are a prediction of work done by Einstein more than 100 years ago, and which has been generally accepted since, the more so as other predictions of that work have already been verified. The first (not counting the precession of the perihelion of Mercury which predates Einstein's ideas) was the deflection of light by the gravity of the sun, measured by Eddington in 1919. Eddington's measurement was in accord with Einstein's prediction, and twice the value that Newtonian gravity would predict. Discovering gravitational waves no more "solves gravity" than Eddington's observations did, less so in my view.

What is more interesting is finding out from what these gravitational waves come. Most of the models involve inspiralling pairs of massive objects (black holes, neutron stars etc). The importance of gravitational waves is that they give us a new window on the physics of these extreme objects.

One thing I don't know is, given the apparent simultaneous detection by more than one detector, how tight is the localisation on the sky. When you can tie the gravitational wave emission to electromagnetic emission (radio, optical, X-ray, gamma-ray) then you can really start to look at new physics.

There was an excellent film on Einstein and Eddington, starring David Tenant and Andy Serkis as the main protagonists, and an excellent supporting cast.