What does Romans 7:25 mean?
In the previous verse, Paul cried out in frustration over his inability to stop sinning even when he wanted to do good. He called himself a wretched man and asked who would deliver him from his body of death.Now he answers that question: Thanks be to God through Jesus Christ our Lord! Paul understands that only God can save him from sin and death and that God does so through faith in Jesus Christ.
This answer is true whether Paul is describing himself as he was before becoming a Christian or after. Only God can release the non-Christian from his slavery to sin by His grace and through his faith in Jesus. Specifically, by faith in Christ, God gives us credit for Jesus' sinless righteousness and takes Jesus' death as payment for our sin.
In the same way, only God can give the Christian the power to set aside our desire to sin and to do what is good and right. Galatians 5 calls this walking by the Spirit, in His power instead of ours. It is the only hope any of us have to serve God in this life.
Paul immediately turns back to the heart of his message, however: He declares that he serves God's law with his mind but his natural, sin-stained body is tempted by the law of sin.