the short answer
Corrective exercise is movement-quality training: work aimed at improving how a healthy client moves, their positions, control and usable range, rather than only how much they lift. Done well, it is the warm-up prep, the sensible regressions and the cueing that help someone own a pattern before they load it hard. What it is not, inside coaching, is treatment. It is not rehab, it is not pain care, and it is not diagnosing what is wrong with a body. That line is the whole point of this entry: movement prep and capacity-building are valuable and firmly in a coach's lane, while diagnosing and fixing people is not. The industry built around corrective exercise has spent years blurring that line, so the honest coaching version is narrower, and far more useful, than the version you may have been sold.
This article is general training education, not medical advice. Corrective exercise as described here is for healthy clients improving how they move. Pain, injury, numbness or anything medical belongs with a physiotherapist or doctor, not a coach.