Part of the quarrels run.
Quick answer
Fires need fuel and quarrels need a supplier. Remove the person carrying the reports and the thing starves.
Read both lines
The mechanism is what makes this useful. A fire does not need to be extinguished if nothing is added, and the saying claims conflict works identically: it is not self-sustaining, it is fed. The NKJV footnotes talebearer as gossip or slanderer, literally a whisperer, and the whisper is the fuel.
The practical implication is hopeful and slightly deflating at once. Most ongoing strife is being maintained by somebody, often somebody who is not a party to it and who experiences themselves as merely informed. Verse 21 will name the same figure from the other end, as the man who kindles. What the verse does not say is worth noticing too. It gives no instruction about confronting the talebearer, and no verdict on the parties quarrelling. It simply identifies the fuel and lets the reader work out that the fire has been burning because someone keeps carrying wood.
Related: Proverbs 26:21 · Proverbs 26:22 · Proverbs 16:28 · Proverbs 22:10
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.