Quick answer
A throne is secured by how the weakest people are treated in court. The verse names the specific practice that makes a reign last.
Read both lines
The book has said several times what establishes a throne, and this is the most specific version. Not military strength, not wealth, not popularity: judging דַּלִּים, the poor, בֶּאֱמֶת, in truth. 16:12 said a throne is established by righteousness and 20:28 said mercy and truth preserve the king. This verse narrows all of it to one courtroom practice.
The reason is not sentimental and the book does not explain it, but the logic is available. A ruler who deals honestly with the people who cannot reward or punish him is dealing honestly by conviction rather than by calculation, and everyone underneath him can see that. Forever is royal-court hyperbole for enduring, the same register as long life elsewhere in this literature, and it is a description of durability rather than a guarantee to any particular king.
Related: Proverbs 16:12 · Proverbs 20:28 · Proverbs 29:4 · Proverbs 31:8–9
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.