Excellent passage, James. Glad you introduced it : )
Paul is a scribe and the Author of this Scripture is employing Paul's particular context to impart truth. The Roman Empire was rife with slavery. Some estimate that 50% of the population under Rome's political sway (Christians included) were enslaved. Paul's inspired application of the politically-significant slavery metaphor is a spiritual one.
Everyone serves someone/something. Spiritually-speaking, there are two options. There is the old nature inherited at birth. And there is the new nature imparted by Grace through faith. The old nature is controlled by law (rules, regulations, etc) or consigned to license (If it feels good...) The new nature is committed to Christ, in Whom liberty is found:
"It is for freedom that Christ has set us free. Stand firm, then, and do not let yourselves be burdened again by a yoke of slavery." (Galatians 5:1 NIV)