Quick answer
Telling the truth under oath saves people. The verse gives ordinary honesty a rescue function.
Read both lines
The NKJV footnotes the first line as saves lives, and that gloss is exactly right: the word is nephashot, lives, the same term this book uses for a person's living self throughout. In a legal setting the stakes were literal, since a false accusation could cost someone their property, their freedom, or their life. What the verse contributes to the chapter is scale. Verse 5 said a faithful witness does not lie, which sounds like a minimum standard; this verse says that same minimum is how people get delivered.
Related: Proverbs 14:5 · Proverbs 12:17 · Proverbs 6:19
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.