What does Hebrews 13:14 mean?

This passage has compared the place of Jesus' execution to the way sacrificial animals were disposed of under the old covenant. Leftover animal flesh was burned outside the camp of Israel (Exodus 29:14). Jesus' crucifixion was performed outside the city walls of Jerusalem (John 19:17–20). In one sense, this continues the way in which old covenant rituals were meant to foreshadow the ministry of Jesus Christ (Hebrews 8:5–6). At the same time, this reminds us that Jesus is being shunned by an unbelieving world. Earlier, readers were encouraged to endure hardship and persecution, knowing that Christ felt the same things (Hebrews 12:2). When the world sees enough of Christ in a believer, it persecutes that Christian the same way Jesus was persecuted (John 15:18–21). Rather than dreading that, believers should rejoice in knowing they're being identified with their savior (1 Peter 4:14).

Here, the writer echoes another point made earlier in the letter. Heroes of the faith such as Noah, Abraham, Isaac, and Jacob trusted in God. A major component of this trust was their understanding of eternity. Rather than seeing everything in a short-term way, those men and women knew that God's ultimate plans for them were eternal. Instead of seeking an earthly home, they recognized themselves as pilgrims on earth (Hebrews 11:13). This verse repeats that point: for the Christian, everything on earth is temporary—including suffering. This is not our home (Hebrews 11:16).