Quick answer
A corrupt country churns through rulers. One person who actually understands things can make stability last.
Read both lines
The first line describes political instability as a symptom rather than a cause. Many princes means rapid turnover, factions, claimants, and the verse traces it back to פֶּשַׁע, the transgression of the land itself, so the churn is what a society's own corruption produces rather than bad luck.
The second line is genuinely difficult in Hebrew and the NKJV supplies "Right" to complete it. What survives every rendering is the contrast between many and one, and between churn and duration. The claim is modest and worth having: stability is not produced by structures alone but by particular people who know what they are doing, and one of them can extend it.
Related: Proverbs 29:2 · Proverbs 28:12 · Proverbs 28:28 · Proverbs 11:14
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.