What is the purpose of shut-off valves (also called cut-out cocks) on a combination vehicle?

AAMVA CDL Manual, Section 6.2.7, p. 6-6

Knowing what a cut-out cock actually does (versus confusing it with other air system parts) matters because misidentifying it during a pre-trip inspection or an on-road air problem can lead to the wrong fix. A driver who understands its real purpose can correctly diagnose why air isn't reaching a trailer.