In today's passage, Paul is trying to convince the Jews of his day that they are allowed to put the old laws away and look to the new covenant made by God through Jesus Christ. The old covenant was a promise that the Jews would be the chosen people of God and they would live in the promised land. The new covenant is so much better - I will give you eternal life and forgiveness. This covenant is available to everyone who believes.
These verses go farther in explaining this new covenant. Paul explains that God no longer wants to issue laws for mankind (who are sinners by nature) to follow. That did not work the first time. Instead, God wants a relationship with each and everyone of us. "No longer will a man teach his neighbor or a man his brother saying 'Know the Lord,' because they will all know me, from the least of them to the greatest."
Paul's point is that this relationship is so much better than the temple hierarchy required by the old laws. He says that the gifts and ministry that Jesus brings is far superior to anything an earthly priest could offer. Even the sanctuary that Moses built (the tent-shrine and the ark of the covenant described in Exodus) was based on his humanly glimpses of God on the mountain and couldn't hold a candle to the heavenly tabernacle awaiting us all.
My favorite verse from this passage comes from The Message and talks about how God describes this new covenant: "This time, I'm writing the plan in them, carving it on the lining of their hearts. I'll be their God and they'll be my people." This is the very essence of God's message to us - always being with us and in our hearts.
I hope today's reading brings you the light of God's promise in your heart.