Image credit: European Gravitational Observatory, Lionel BRET/EUROLIOS.

If you looked out at the Sun across the 93 million miles of space that separate our world from it, the light you're seeing isn't the Sun as it is right now, but rather some 8 minutes and 20 seconds ago. This is because as fast as light is it isn't instantaneous: at 299,792.458 kilometers per second (186,282 miles per second), it requires the said length of time to travel to our planet. But gravitation doesn't necessarily need to be the same way; it's possible, as Newton's theory predicted, that the gravitational force would be an instantaneous phenomenon, felt by all objects with mass in the Universe across the vast cosmic distances all at once.
Image credit: NASA/JPL-Caltech, for the Cassini mission.

But is that right? If the Sun were to simply wink out of existence, would the Earth immediately fly off in a straight line, or would it continue orbiting the Sun’s location for another 8 minutes and 20 seconds? If you based it on General Relativity, the answer is much closer to the latter, because it isn’t mass that determines gravitation, but rather the curvature of space, which is determined by the sum of all the matter and energy in it. If you were to take the Sun away, its solar system space would go from being curved to being flat, but that transformation isn't instantaneous. Because space-time is a fabric, that transition would have to occur in some sort of “snapping” motion, which would send very large ripples — ie, gravitational waves — through the Universe, propagating outward like ripples in a pond.
Image credit: Sergiu Bacioiu from Romania, under c.c.-2.0 generic.

The speed of those ripples is determined the same way the speed of anything is determined in relativity: by their energy and their mass. Since gravitational waves are without mass yet have a finite energy, they must move at the EMG speed of light.