What does Hebrews 13:13 mean?

A dominant theme of the book of Hebrews has been the need to "hold fast" to faith in Christ, despite persecution (Hebrews 3:6; 4:14; 6:18; 10:23). The evidence given in this letter proves the superiority of the new covenant in Christ, over the old covenant of animal sacrifices. The components of the old covenant were all meant to symbolize something important about the ministry of Jesus Christ (Hebrews 10:1). In earlier verses, the writer extended this analogy to the way Jesus was taken outside the city walls of Jerusalem for His execution (John 19:17–20). This parallels how the animals sacrificed to consecrate Aaron's priesthood were also taken outside the camp to be burnt (Exodus 29:14).

Even when Christians face difficulty, this is not a sign of failure; it's often part of God's plan to grow our faith (Hebrews 12:3–11). And, persecution is expected for believers living in a fallen world (John 15:18–21). Rather than despairing when that hardship comes, or running from it, we should embrace being identified with Christ. Elsewhere in the New Testament, we're told that persecution which comes because we're so closely identified with Christ is a sign of our relationship with Him (1 Peter 4:14).