What does Hebrews 13:3 mean?
Prior verses listed practical instructions for Christian believers. These included demonstrating brotherly love (Hebrews 13:1) and care for strangers (Hebrews 13:2). Love for fellow Christians is consistently mentioned in the Bible as proof of one's faith (John 15:12; 1 John 4:20). Scripture not only contains Jesus' teaching that our attitude toward strangers reflects our attitude towards Him (Matthew 25:35–40), it also includes stories where those strangers were actually angels (Genesis 19:1–3).This verse completes a series closely resembling Jesus' words in Matthew 25. There, He indicated the need for Christians to care for the needy, strangers, and those in prison. Prior verses mentioned fellow believers and strangers, and here Christians are commanded to care for those in prison. This letter was written to persecuted Jewish Christians, though it pointedly notes that those originally reading the letter have not suffered as much as have other believers (Hebrews 12:4). Those who are actually being deprived of freedom, rights, or property deserve the support and sympathy of believers.
The writer of Hebrews also includes those who are "mistreated" in his commands. This is from the Greek term kakouchoumenōn, used only twice in the New Testament. The other occurrence is in Hebrews 11:37; it applies to examples of those with godly faith suffering persecution and martyrdom. This meshes well with a major theme of the book of Hebrews: that believers ought to "hold fast" through suffering, while keeping in mind the sufferings of others for the sake of Christ.