The writer of Hebrews describes a difference between the Jewish sacrifices and God's Lamb the Lord Jesus: the sacrifices of atonement where the blood was presented before God were completely consumed with nothing left. Their carcasses were burned outside the camp.
But our Lord Jesus' sacrifice remains meat and drink for His people! In His Sacrifice is all our hope for eternal life and salvation!
Thus, the Jewish sacrifices, once offered, were of no lasting value, but another sacrifice had to be made, and another and another, because they could never take away sin.
But Christ's sacrifice, though it was made only once, has a perpetual benefit for the Saints.
The old sacrifices were abandoned outside the camp. Our Sacrifice draws us unto Himself perpetually and forever! There was no life or food in their sacrifices, but our Sacrifice is our life and our food for eternity!
The Jews rejected Christ when He died, believing falsely that He was no use to them anymore. Like their animal sacrifices, they discarded Him outside the city walls at Calvary.
But we know better, and ought to cling to Him, though rejected by men, and forsake everything else as of little value.
The Old Testament contains many references to the dishonor of the place outside the camp. The phrase has a double first mention, both of which are startling in comparison to this last mention in Hebrews.
The writer of Hebrews uses this metaphor of "outside the camp" to show Hebrew believers the true nature of the choice they must make to stay with Christ or return to society, privilege, acceptability, and respectability of the apostate Jewish faith.
Where Christ is, is far better!