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 'messengers' of information provides scientists with a different but complementary view of the Universe.
Gravitational waves, however, are fundamentally unrelated to EM radiation. They are as distinct from light as hearing is from vision. Imagine if humans were a species that only had eyes to observe and understand the Universe. You can learn a lot simply by studying the light from objects (astronomers have done this extraordinarily well in the last century). Then one day, someone invents something called an "ear", which senses distant vibrations in air or water, vibrations that had been there all along but you could not detect simply by using your eyes. Consequently, this new ear enables you to learn things about your world (and ultimately, the Universe) that you would never have gleaned from light. This is how LIGO has opened a new 'window' on the Universe. LIGO is a gravitational wave antenna, able to detect vibrations in the 'fabric' of space-time itself, emanating from the farthest reaches of the cosmos. Things like colliding black holes, which are utterly invisible to EM astronomers, are beacons in the vast cosmic sea to LIGO and other gravitational-wave detectors like it.
More importantly, since gravitational waves interact very weakly with matter (unlike EM radiation, which can be absorbed, reflected, refracted, or bent by gravity itself), they travel through the Universe virtually unimpeded, carrying information about their origins that is free of distortion.
The gravitational waves that LIGO detects are caused by some of the most profoundly cataclysmic 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 un-seeable wonders. LIGO has removed a veil of mystery on the Universe, and in so doing, has ushered in exciting new research in physics, astronomy, and astrophysics.