The woman caught in adultery represents all of us. Jesus stands in our place, taking our condemnation for sin, enduring it's punishment of death, so we may live. We are all sinners, guilty of being unfaithful to God's Love. Yet with the new life Jesus wins for us, we can "Sin no more" if we live in His love, in relationship with Him, and avoid anything that would harm that relationship, or separate us from Him.