This is how Eugene Peterson paraphrases part of those verses in The Message:
The time is coming when I will make a brand-new covenant...I will put my law within them—write it on their hearts!—and be their God. And they will be my people. They will no longer go around setting up schools to teach each other about God. They'll know me firsthand, the dull and the bright, the smart and the slow. I'll wipe the slate clean for each of them. I'll forget they ever sinned!"
When we partake of the cup at the table during our weekly time of worship, we are reminded, "This cup is the new covenant in my blood..." The blood that washed our sins away seals us with God's new covenant. We are His. His law is written on our hearts.
And what is that law? Love. Love Him, love ourselves, love others likewise. All right actions--compassion, obedience, justice, mercy, peace, goodness, honesty, self-control, etc.--come from living in love. Our heart is sealed--like an letter from the King, stamped with His seal in sealing wax--that we are His, and He is ours. As we wait in Advent, let us listen to our heart--what it truly says, what God has imprinted upon it.