We will focus on the word translated as "right." The King James Version reads "power." This is exousia (Strong's #1849), which has a variety of usages: "power," "authority," "capability," "ability," "strength," "entrusted," "commissioned." It implies the liberty or power to do something. This Greek word has its roots in exesti. The two of them, exesti and exousia, combine two different ideas, "right" and "might." A person can be given the right to do something and then given the might or power to do it. What does God do here through Jesus Christ? As many as receive Him, to them He gives the right and the power to become children of God.
John W. Ritenbaugh
Faith (Part 5)