What does Hebrews 13:12 mean?

When Jesus was crucified, the execution took place outside the walls of the city of Jerusalem (John 19:17–20). In the prior verse, the writer of Hebrews noted that leftover flesh from sacrificed animals was burned outside the borders of Israel's camp, under the old covenant (Exodus 29:14). This letter has also shown how the physical components of the old covenant, including the temple and sacrifices, were meant to symbolize the "real" sacrifice of Jesus Christ (Hebrews 9:23–24). Here, that idea is applied to the concept of being discarded, cast out, or rejected.

Just as animals were killed to consecrate Aaron and the priesthood, so too did Jesus die to consecrate those who believe in Him. This symbolic "casting out" was meant to imply something negative: the thing being discarded was unfit, unclean, or unwanted. Jesus willingly endured that kind of hatred (Hebrews 12:2), for our benefit. A major theme of the book of Hebrews has been the need to "hold fast" despite persecution. So, even when the world—or our own culture—hates and rejects us, we ought to be willing to "go to Him" (Hebrews 13:13) in that state, preferring God and His kingdom over the approval of other men (Hebrews 13:14).