Since we are under grace and not the law, why not just go on sinning? And why not worship ourselves rather than our Creator? These are the questions Paul had to answer. He does so using an analogy of slavery. We are slaves to the one we obey. If we continue obeying sin and worshiping ourselves, our lives will end in eternal death. On the other hand, if we are slaves to God, we will find righteousness and, ultimately, eternal life.
Since all who believe the Gospel are united with Christ in His death and resurrection, believers are no longer slaves to sin. It is like we have died to it. When Jesus Christ is real to you, every part of your life begins to reflect that. Sin and self-worship no longer have dominion over you.
Apart from Christ, we were slaves to impurity and ever-increasing wickedness leading to death. But now, in Christ, we have been set free from sin. The only One we are bound to now is our Lord. And being a slave to God does not oppress us or shackle us; it leads to holiness and eternal life.