"Blessed is he whose transgression is forgiven, whose sin is covered. Blessed is the man unto whom the Lord imputeth not iniquity." (Psalm 32:1-2)
The Hebrew word translated in this verse as "covered" (kacah) appears elsewhere as "hid" (Psalm 32:5). The idea is that you don't see it anymore because something else has been positioned, superimposed, placed atop and hiding it from view. And as this is the Old Testament, the idea of covering sin is about as high as it got. David had insights that were ahead of his time, however: "As far as the east is from the west, so far hath He removed our transgressions from us." (Psalm 103:12)
"Wash me throughly from mine iniquity, and cleanse me from my sin. For I acknowledge my transgressions: and my sin is ever before me." (Psalm 51:2-3)
But with the advent of Jesus, God the Father amended a feature that allowed us to gain a standing before Him that is lightyears ahead of anything we could ever look to carve out on our own. As the system was irrevocably broken because of original sin, coupled with the legalese accompanying the worldwide project begun under God's sponsorship, the whole model would now need to be overhauled. Fast-forward to the Greek of the New Testament. Now we read things like this:
"And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with Him, having forgiven you all trespasses; Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to His cross." (Colossians 2:13)
Can you imagine the joy and the wonder that Paul experienced having been shown these finer points of the Gospel of Jesus Christ? The dawning realization that there was something deeper at work than the long-held and revered traditions of the Law? To begin to glimpse a vista in which the legalese keeping us tied to animal sacrifice as a means of atonement...has dissolved? Something you can read about and think about but not really feel until you bring to God any guilt you might sense for analysis. The mere words don't do it justice, if that makes sense. This idea that you are forgiven beyond all imagining, now and forever, is something that has to be believed and then experienced for yourself.
Got you covered
The hard outer coverings of, say, a ladybug, are called elytra (singular: elytron). The word is Greek in origin and means "covering" or "sheath". It isn't the same "covering" spoken of by Paul in his first letter to the Corinthians (11:15), however. The word in that verse refers to "something cast all around". It's that and more and with the coverage we have under God's new covenant. The words in God's contract with the human race and ratified by Jesus' life and death speak to a standing that anyone BC didn't get to experience. When Jesus went and "preached unto the spirits in prison" (1 Peter 3:19) these new terms, a brand new paradigm had been drawn up and propagated. The finest print you could ever imagine. It'd take years and years to read all the context. Or! One could simply believe that Jesus is and did what the Bible says He did and does.
There's a lot to this. Just think of Jesus walking through the leaves of the Bible looking to tell you for yourself that which you need to know to appropriate all He wants to give you. I don't know how else to say it. The unraveling of all our shortcoming and mistakes and wrongdoing is now a reality. Something that comes as a bonus of having met the Lord.
"For if our heart condemn us, God is greater than our heart, and knoweth all things. Beloved, if our heart condemn us not, then have we confidence before God." (1 John 3:20-21)