Quick answer
Refusing correction is an act of self-contempt, whatever it feels like at the time. Taking it is how a person acquires the very thing he was missing.
Read both lines
The first line makes an unexpected identification. Rejecting instruction feels like defending yourself, protecting your competence and your dignity, and the verse says the opposite is happening: the man is despising his own soul, treating himself as not worth the trouble of improvement. The second line supplies the payoff, and the Hebrew is better than the English. "Gets understanding" is literally acquires heart, which uses the same purchase verb that drove the father's "Get wisdom" in Proverbs 4 (4:5, 4:7) and answers the man at 15:21 who was destitute of heart, literally missing one. So the chapter's arc closes: the fool lacks a heart and enjoys the lack, and the man who can hear a rebuke buys one.
Related: Proverbs 15:21 · Proverbs 4:7 · Proverbs 19:8
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.