the short answer
Kinesthetic awareness is your sense of where your body is and how it is moving, without looking - the felt, usable version of movement. It is built on proprioception, the raw position signals your joints and muscles send, but it is the conscious layer you can actually notice and adjust. A client with sharp kinesthetic awareness feels a hip that shot up early or a knee that caved in and can correct it from a single cue. A client without it stares at you, honestly unable to feel the thing you just described. The good news for coaching is that it is a trainable skill, it improves with practice rather than talent, and a few simple methods build it fast.
This article is general training education, not medical advice. If a client has dizziness, a balance problem or any health condition affecting movement, have them work with a qualified professional before adding balance or eyes-closed drills.