Quick answer
Hatred keeps conflict alive by keeping offenses in circulation; love takes offenses out of circulation by covering them. This is the proverb behind "love covers a multitude of sins," and covering means absorbing a wrong rather than broadcasting it, not concealing abuse or evading justice.
Read both lines
The two lines describe two economies of offense. In the economy of hatred, every offense is capital: collected, invested, brought out at the right moment to stir the pot again. Hatred does not even need new grievances; it can run indefinitely on old ones, because stirring is the point.
In the economy of love, offenses are covered. The Hebrew verb is the ordinary word for covering something over, and the picture is of a wrong that love chooses to absorb rather than publish. Not because the wrong was fine, but because love would rather bear a cost than start a cycle. Both Peter and James reach for this proverb ("love will cover a multitude of sins," 1 Peter 4:8; James 5:20), which tells you the early church treated it as a load-bearing wall.
What it does not mean
"Covers" has been misused to demand silence from the harmed: keep the abuse quiet, protect the institution, that is what love does. It cannot responsibly mean that. Proverbs itself despises the concealment of injustice and defends the vulnerable loudly (24:11–12, 31:8–9). Covering is what love does with the ordinary friction of living with sinners, the insult, the slight, the failure, absorbed instead of amplified. Protecting a wrongdoer's access to victims is not covering sin; it is joining it. The same book that wrote this verse also wrote that partiality toward the wicked is not good (18:5).
From this side of the cross
The proverb is about interpersonal love, and it should be received as such. But because your sins were already forgiven in Christ, covering an offense is never a payment toward your own forgiveness; it is what forgiven people can afford to do. Covered people are free to stop keeping score.
Related: Proverbs 17:9 · Proverbs 19:11 · 1 Peter 4:8
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.