M-S decoding lets you adjust stereo width after recording by changing the mid-to-side ratio
In M-S recording the mid channel (cardioid) captures the center of the scene and the side channel (figure-8) captures the difference signal. Decoding requires copying the side signal to two channels and inverting one, then panning them hard left and right. Crucially, adjusting the relative level between mid and side faders controls stereo width continuously: more side = wider image, less side = narrower. This post-recording control is impossible with X-Y or ORTF. Many stereo mics include an internal M-S matrix with a switch or dial for mid-side ratio. The decoded stereo output is mono-compatible at any width setting because the side signals cancel when summed.
Examples
Using three faders on a mixer: mid centered, side+polarity-flipped hard left, side normal hard right. Pull down the side faders to narrow the image without touching the mid. In a DAW, this is achievable with a utility or MS matrix plugin.
Assessment
Given an M-S recording, describe what happens to the stereo image as you gradually reduce the side fader level to zero. Distinguish M-S from X-Y in terms of post-recording flexibility.