When the interferometer starts to rotate e.g. clockwise the clockwise propagating laser beam has to cover more distance because the detector is moving away. The counter-clockwise propagating beam has to cover less distance as the detector is moving towards it. Now the two laser beams have a different phase at the point where they interfere resulting in a different amplitude of the signal at the detector.
In this interferometer the laser beams are propagating through a silica fiber (the same that are used for telecommunication purposes) and the detector signal is used to adjust the frequency of an audio signal which is transmitted to the speakers.
(Gruppe Arno Rauschenbeutel, ATI, TU Wien)