Now without getting too bogged down in Hebrews, which would be easy to do given the tremendous depth of the book and its application to our lives, these scripture passages are identifying that Jesus came to offer up His blood as a final sacrifice as our High Priest. It also says that a testament is in force after someone has died and after the shedding of blood. Notice the parallels that say that Jesus is our High Priest (8:1; 9:1). Also notice the reiteration that Jesus came to be the Mediator of a better covenant (8:6; 9:15). Now finally, read Hebrews 10:12-23:
12 But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God,
13 from that time waiting till His enemies are made His footstool.
14 For by one offering He has perfected forever those who are being sanctified.
15 But the Holy Spirit also witnesses to us; for after He had said before,
16 “This is the covenant that I will make with them after those days, says the Lord: I will put My laws into their hearts, and in their minds I will write them,”
17 then He adds, “Their sins and their lawless deeds I will remember no more.”
18 Now where there is remission of these, there is no longer an offering for sin.
19 Therefore, brethren, having boldness to enter the Holiest by the blood of Jesus,
20 by a new and living way which He consecrated for us, through the veil, that is, His flesh,
21 and having a High Priest over the house of God,
22 let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience and our bodies washed with pure water.
23 Let us hold fast the confession of our hope without wavering, for He who promised is faithful. (NKJV)