The point is to decorrelate the channels. The left and right channels are usually mostly the same, so coding them both would basically send the same signal twice. With perfect decorrelation, the side channel would become zero, instantly saving half the bits.

(It's the same idea for images, where the RGB channels mostly all look like grayscale copies of the image, so the YCbCr/YCoCg transform is done to decorrelate them.)

There are actually three methods in FLAC: mid/side, left/side, and right/side. Each frame can use a different method and stores what method it used (if any) in the frame header.

The difference has a range 1 bit larger than the original, but this doesn't matter that much since everything is getting compressed anyway. Anyway the bit is only used if the side channel is very large, ie. the correlation was poor, in which case it would be better not to use a decorrelation for this frame.

Interchannel Decorrelation: https://www.ietf.org/archive/id/draft-ietf-cellar-flac-04.ht...

Channel Bits in Frame Header: https://www.ietf.org/archive/id/draft-ietf-cellar-flac-04.ht...