In addition to confirming Einstein's prediction the discovery of gravitational waves opens new ways for studying the universe. We have been observing the known universe by looking at various frequencies of light and that's gotten us surprisingly far.
Looking at the gravitational waves generated by truly colossal events like black hole collisions will allow us to look at extremely energetic processes from a gravitational perspective. These processes can in turn give us hints as to what space time is made of at its basic levels and how gravity fits in with the rest of our understanding of the world.
New theories that try to reconcile quantum theory with Einstein's relativity all have to make predictions about the detailed gravitational wave signature of these processes. Based on the predictions gravitational wave detectors will allow us to pick the correct theories, furthering the reach of physics, and eventually giving the engineers something to build (like your warp drives, which are
allowed by general relativity to begin with).
TL;DR It's a big deal for mankind, but it likely won't affect you personally. Time travel might still be a no-no, but looking at gravitational waves might change this.