The advantage of an FM stereo signal over a monaural signal in communication systems is that you can transmit and receive two channels of information at the same time. Typically, this is the left and right audio signal, and it allows the listener to perceive spatial aspects of the original performance.
This is done by sending left+right over the base modulation range. A monaural receiver will then play left+right over one speaker, making it compatible with older receivers.
Then, to get the second channel, we send left-right over a secondary modulated carrier of 38kHz, riding on top of the original modulation. The receiver decodes that by adding and subtracting. In one case, left+right plus left-right gives 2 times left, and left+right minus left-right gives 2 times right.
There is also a 19kHz pilot tone included, which a receiver can detect and use to enable the decoder. This will help the receiver not attempt to decode when there is a weak signal.