These verses are a writer's prayer for God to KNOW their whole being: heart, mind, and body.
First, it’s a prayer to “know my heart.” Think about every time you’ve ever been misunderstood. You said something that came out wrong or did something with good intentions that someone took the wrong way. When you're known by a God who knows your heart, you can have 100% confidence that He sees the best in what you say, do, and think, always.
Next, it’s a prayer that God would “know my anxious thoughts.” You know what I'm talking about. The ones that you’re too embarrassed to tell most people. And the people you do tell you probably don’t REALLY tell. Being known by God is being understood. It’s being validated. He’s actually worried about what you’re worried about, and your worries are completely legitimate to Him!
Finally, it’s a prayer that God would know our actions, even the ones we’re not proud of (our “offensive ways,” or sins). Uh, scary! Why would I want God to know about the way I treated that friend at lunch or the party I went to last week? Wouldn’t that be the last thing I want God to know about me?
But here’s the thing: this isn’t a prayer for God to judge the worst of the worst things you’ve done. It’s a prayer that God would know every last part of you: the good, the bad, the ugly, and the really ugly. Yet, God knowing you isn’t a threat! Read that last line one more time. Why do we praise God that He knows every little thing about us? Because when God knows us, He can lead us.
And where is He taking us? The way everlasting—when God knows us, He leads us to the good life, the full life, the eternal life. That is what it means to be known by the God who loves you more than you could possibly understand.