Why Detect Them?
Historically, scientists have relied almost exclusively on electromagnetic (EM) radiation (visible light, X-rays, radio waves, microwaves, etc.) to study the Universe (some are trying to use subatomic particles, called neutrinos, as well). Each of these sources of information provides scientists with a different but complementary view of the Universe.
Gravitational waves, however, are completely unrelated to EM radiation. They are as distinct from EM radiation as hearing is to vision. Thus, they are unique messengers of information about cosmic events. Having this new 'sense' with which to observe the Universe is important because things like colliding black holes are utterly invisible to EM astronomers. To LIGO, however, such events are beacons in the vast cosmic sea.
More importantly, since gravitational waves interact very weakly with matter (unlike EM radiation), they travel through the Universe virtually unimpeded, giving us a clear view of the gravitational-wave Universe. The waves carry information about their origins that is free of the distortions or alterations suffered by EM radiation as it traverses intergalactic space.
The gravitational waves that LIGO detects are caused by some of the most energetic events in the Universe—colliding black holes, merging neutron stars, exploding stars, and possibly even the birth of the Universe itself. Detecting and analyzing the information carried by gravitational waves is allowing us to observe the Universe in a way never before possible, providing astronomers and other scientists with their first glimpses of previously unseen, and until now, un-seeable wonders. It has opened up a new window of study giving us a deeper understanding of cataclysmic events and ushered in exciting new research in physics, astronomy, and astrophysics.