What does Hebrews 13:15 mean?

This letter to persecuted Jewish Christians is meant to encourage. Their faith is in a superior covenant, brought by Jesus Christ (Hebrews 9:13–14). As a result, even when suffering, believers ought to "hold fast" to that trust in God (Hebrews 3:6; 4:14; 6:18; 10:23). Prior heroes of the faith looked beyond this life to eternity (Hebrews 11:13), which helped them endure temporary hardships on earth (Hebrews 11:35–38). In the same way, Christians ought to expect persecution from the world (John 15:18–21), and choose to be "cast out" with Christ when necessary (Hebrews 13:10–13). And, we should be looking forward, to heaven, rather than excessively worrying about what happens here on earth (Hebrews 13:14).

This verse contains another practical result of this teaching. Believers ought to offer a sacrifice—but one of praise, not animals or materials. Since Jesus' work on our behalf is completely finished (Hebrews 9:24–26), there is nothing we can add to it (Galatians 3:10–14). Instead, our praise and sacrifice ought to be done out of gratitude, obedience, and worship. The following verse expands this idea to remind believers that doing good for others is a natural, expected part of this joyous perspective.