Gravitational waves were predicted by Einstein to explain how two things millions of miles apart can be aware of each other (think, why the Earth goes around the sun). Basically, it is a ripple in the fabric of space-time itself that everything with mass gives out, and bigger things give off bigger ripples. These ripples are predicted to travel at the speed of light- so, to go back to the Earth-Sun example, if the Sun disappeared this second you would have a 7 minute delay where the Earth would keep going on its orbit as if the Sun were still there.
Now, LIGO. These guys did an amazing experiment where they basically had two stations, one in Louisiana and one in Washington State, where you're basically shooting a laser down a several mile long tunnel in a hope to see a ripple as a gravitational wave passed through. This is insanely precise work- as in, as precise as a human hair's diameter over three light years from Earth. What's more, this is only sensitive right now to the biggest, strongest gravitational wave signatures right now, such as black hole mergers- so we are not detecting planets with this anytime soon for example- but hey, gotta start somewhere!
Finally, I can't emphasize how huge this is! We are literally going into a new era of astronomy right now, and I think that's no exaggeration. Think of it this way, most of astronomy right now has been done with light, ie electromagnetic waves- with some exceptions, like cosmic rays or space missions- but pretty much all astronomy has only been with EM waves. Now we will literally have a new tool in our toolkit and will likely learn all sorts of new things we won't have even expected. I can't wait!
