The reason there are two LIGO observatories is that if a gravitational wave event is truly detected at one observatory, then it will be detected at the other observatory. This dual detection rules out the event as a local "noise" event, and helps to pinpoint the outer space source of the event using triangulation.
The realization of the LIGO concept is quite difficult, because the tunnel path length difference for even a relatively large gravitational wave is incredibly small. Additionally, there are all kinds of "noise" that must be ruled out when a possible event takes place, specifically vibrational "noise" from local vehicular traffic, or "noise" from seismic events.
The concept of LIGO is relatively simple: if a gravity wave of sufficient strength hits the Earth from outer space, one of the tunnels will temporarily become slightly shorter than the other. This temporary difference in light beam path lengths for the two tunnels should create a measurable change in the normal interference result for the two beams. Click here to see an animation on wave interference.
The LIGO observatories are composed of two laser beams, one for each of two high vacuum tunnels. The beams are shining at a common target, with the two tunnels connected to each other so as to form an "L" shape. The two beams are controlled in such a way that they "interfere" with each other, much like two waves interfere with each other so as to form a common wave, a wave that is the arithmetic sum of the two original waves.
The LIGO observatories are designed not to detect light (i.e., electromagnetic radiation), but gravity waves, something completely different.
There are two LIGOs in the United States: one in Louisiana, and the other in Washington State.
LIGO is an acronym for Laser Interferometer Gravitational-Wave Observatory.