When I was in Israel some years ago, I saw a little Israeli boy chasing after his dad, calling out, "Abba! Abba! Abba!" I knew what that meant. It would be the same as if we saw a child in the U.S. chasing after his father saying, "Daddy! Daddy! Daddy!" "Abba" is a Hebrew word that speaks of affection and intimacy between a parent and a child.
Not only has God forgiven us, justified us, and given us free access into His presence, but He also has adopted us into His family. The Bible tells us,
But when the fullness of the time had come, God sent forth His Son, born of a woman, born under the law, to redeem those who were under the law, that we might receive the adoption as sons. And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out, "Abba, Father!" Therefore you are no longer a slave but a son, and if a son, then an heir of God through Christ. (Galatians 4:4–7)
I can stand in awe of a God who has the power and desire to forgive me and put His righteousness into my account. But by adopting us, God is going further. He is saying, "Don't just stand there in awe of me. Come close to me." Adoption speaks of a close relationship. God says, "I want you as my son. I want you as my daughter."
It's amazing to think of approaching the Almighty God and saying, "Abba." But you see, God is saying, "I want you to come close. And from now on, you have a new relationship. You are part of the family of God forever, because of your faith in Jesus Christ.