Quick answer
Integrity lets you walk without watching your back, because there is nothing behind you to surface. The crooked man lives with a countdown: what he has twisted will come out.
Read both lines
The person of integrity walks "securely" not because the road is smooth but because he is not carrying a secret that can detonate. He can be audited; his story does not require management. That is a form of peace money cannot buy. The second line is quietly ominous: the one who perverts his ways "will become known." Not necessarily punished, not necessarily today, just, eventually, seen. Every crooked path is a bet that exposure can be outrun forever, and the proverb states the odds on that bet.
From this side of the cross
One sentence here, because the verse mostly needs no help: the gospel is what makes total honesty survivable, since the person already fully known and fully loved has nothing left to hide.
Related: Proverbs 28:1 · Luke 12:2
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.