Quick answer
Words come from somewhere deep, and wise words keep coming: speech rises from a person's hidden reservoirs, and wisdom's spring stays fresh and flowing.
Read both lines
The first line claims all speech for depth: words are drawn from the person's hidden places, character and history and heart, depths the speaker himself may not have mapped. The second line focuses the contrast: the wellspring of wisdom is a flowing brook, fresh, moving, continuously supplied. Deep is not automatically good; a well can hold anything. The wise person's distinctive is source and renewal, a spring producing clean water in every season, and the book has named the supply line already: the heart of the wise teaches his mouth (16:23).
Related: Proverbs 16:23 · Proverbs 20:5 · John 7:38
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.