Albert Barnes Commentary Galatians 4:5

"that he might redeem them that were under the law, that we might receive the adoption of sons." — Galatians 4:5 (ASV)

To redeem them. By his death as an atoning sacrifice. (See Barnes on Galatians 3:13).

Them that were under the law. Sinners, who had violated the law, and who were exposed to its dread penalty.

That we might receive the adoption of sons. Be adopted as the sons or the children of God. (See Barnes on John 1:12; Romans 8:15).