Albert Barnes on Hebrews 13:11

For the bodies of those beasts, etc. The word here rendered "for"--γαρ--would be here more properly rendered "moreover." Stuart. The apostle is not urging a reason for what he had said in the previous verse, but is suggesting anew consideration to excite those whom he addressed to fidelity and perseverance. In the previous verse the consideration was, that Christians are permitted to partake of the benefits of a higher and more perfect sacrifice than the Jews were, and therefore should not relapse into that religion. In this verse the consideration is, that the bodies of the beasts that were burned were taken without the camp, and that in like manner the Lord Jesus suffered without the gate of Jerusalem, and that we should be willing to go out with him to that sacrifice, whatever reproach or shame it might be attended with.

Whose blood is brought into the sanctuary, etc. Heb 9:7,12.

Are burned without the camp. Lev 4:12,21, 16:27. The "camp" here refers to the time when the Israelites were in the wilderness, and lived in encampments. The same custom was observed after the temple was built, by conveying the body of the animal slain for a sin-offering, on the great day of atonement, beyond the walls of Jerusalem to be consumed there. "Whatever," says Grotius, "was not lawful to be done in the camp, afterwards was not lawful to be done in the city."

(a) "without the camp" Lev 16:27