It’s not what everyone else thinks about you that matters. People may believe you to be a person of integrity, or never, ever hear you say anything bad – but they are not your judge, because they don’t know all of your words and thoughts, do they? That is why David prays in Psalm 19:14, “Let the words of my mouth, and the meditations of my heart be acceptable in YOUR sight, O Yahweh, my Rock and my Redeemer.”
David says his goal is not that his words and thoughts would be acceptable to other people, but to God. In Hebrew the first words of the verse are actually “Be acceptable”, emphasizing that it is finding that acceptance that is the priority. And the acceptance he is seeking is not from men, but from God; literally, “to Your face, Yahweh.”
Other people do not know your “hidden faults” (which David had mentioned just earlier in :12) but God does. That is why the fact that this verse teaches that our righteousness must be in His sight would be absolutely condemning to us — for He knows all of our words and every thought! — UNLESS we have some righteousness other than our own for Him to see. Thankfully, in Jesus Christ we DO have “the righteousness of God through faith in Jesus Christ for all those who believe.” (Romans 3:22)
We should still strive that our every word and thought might please God and not merely men. But we can also be grateful that through Christ, God is our “Redeemer” who has hidden us in Christ in His sight (Colossians 3:3) and sees only His perfect righteousness when He examines us!