When you place an object on the fabric, the cloth curves. This is exactly what happens in the solar system as well.
The sun with such a huge mass bends the space-time fabric. And the earth and all the planets are kept in orbit by following this curvature that has been made by the sun. Depending on the various masses of objects, the way they bend this fabric also varies.
All this is most certainly easily said than done and requires meticulous and extensive research, not to mention highly sensitive instruments.
Had they not have measured this time difference, we might have had to wait for the merger for more massive black holes to collide and maybe even build more sensitive instruments to detect these waves..
Why is this discovery a Big Deal ?
Gravitational waves gives us another way to observe celestial phenomenon. These waves also form when supernovae explode, when black holes collide and during many other space activities.
Detecting them might give us a new perspective into the cosmic events. There is hell of a lot of space that is left unexplored or lies beyond human exuberance and this discovery might shed some light on it. ( like the big bang per se )
The ultimate goal is to understand the fundamental laws of the universe. It is a quest through the oblivion towards a theory of everything.
Although it is unknown how many years/decades it might take to get us there, but these discoveries are markers to getting there.
And Einstein predicted this a 100 years back!
Note: Hope you are able to understand and appreciate the profundity of the discovery done by mankind from this post. It is truly an amazing moment to be alive.