Hebrews 8:1 pauses to name the main point: we have such a high priest, who sat down on the right hand of the throne of the Majesty in the heavens. Sitting matters. Earthly priests never sat while serving, because their sacrifices were never finished. Jesus is enthroned. He is a servant of the sanctuary and of the true tabernacle which the Lord pitched, not man.
Verses 3 to 6 compare two ministries. Earthly priests offered gifts according to the law, but they served a copy and shadow of the heavenly things. God warned Moses, See, you shall make everything according to the pattern that was shown to you on the mountain. The tabernacle was designed to point beyond itself. By contrast, Jesus has obtained a more excellent ministry, because he is the mediator of a better covenant built on better promises.
Verses 7 to 13 quote Jeremiah 31:31-34. The problem with the first covenant was the people, who did not continue in it. So God promised something deeper. I will put my laws into their mind; I will also write them on their heart. I will be their God, and they will be my people. Everyone will know the Lord, from least to greatest, and the promise rests on forgiveness: For I will be merciful to their unrighteousness. I will remember their sins and lawless deeds no more. By calling it new, God made the first covenant old, and what grows old is near to vanishing away.