Paul here gives a conclusion to verses 1-6. Before God's calling, we were servants—slaves—to sin and Satan (Romans 3:9; 5:12; 6:1-23; Ephesians 2:1-3). This present system of things, under Satan, was our "tutor" and "governor," not for instruction or safe-keeping but for keeping us controlled and limited. When we were spiritually immature—"children"— we were in bondage to the foundational principles and elements of this world.
At the time when God chooses, He calls us out from this cosmos, this world apart from Him. This is possible because Jesus Christ's atoning sacrifice bridges the gap, caused by sin, between God and the man that He chooses and causes to approach Him (Psalm 65:4). Christ became the "curse of the law," the penalty of death, for us and redeemed us from Satan and from sin's grasp so that we could begin to have a relationship with our Creator. Through the legal action of justification, God brings us into alignment with His holy law and takes away our sins and the eternal consequence of them—but He does not take away the law anymore than a civil governor does away with the law against murder when he gives a last-minute reprieve to a murderer.
To those individuals who hear and properly respond to God's summons, He gives the opportunity— the right!— to become His sons: "But as many as received Him, to them gave he power [authority] to become the sons of God, even to them that believe on his name" (John 1:12). This is symbolized by adoption, because Paul is emphasizing that prior to this time, we had another father—a supernatural being whose image we bore, whose deeds we followed, and whose words we spoke. It was this father that enslaved us, and it was his system that we all willingly participated in before God's intervention.
It was this system that the Galatians were returning to and which Paul was speaking against (Galatians 4:3, 8-11). Because of the price that Christ paid, God purchased those individuals that He has a plan for, and thus they became His "adopted" sons and heirs—but not yet inheritors—to the promises made to Abraham and to the Kingdom.