Francis Schaeffer comments on this passage in The Finished Work of Christ...
We have received the Holy Spirit, and we are to let Him lead us. If we are truly saved, there should be some evidence of this in our lives. But Paul isn't saying these things to make us grovel in sorrow, searching our hearts and beating our chests, wondering, “Am I really a Christian?” We will see that the rest of this chapter is a great cry of victory and assurance. If you are indwelt by the Holy Spirit, then indeed you should walk in the Spirit and you should be led by the Spirit. At the same time, interwoven with these reminders is the tremendous realization that, having accepted Christ as Savior and being indwelt by the Holy Spirit, God is our Father. [8:15-17] He loves us and cares for us.
If we have accepted Christ as our Savior, God the Father, the Creator, the very one we have sinned against, can now be called “Daddy.” [8:15] Paul has pointed out the absolute gap between being saved and being lost. He has reminded us of the importance of recognizing that we are indwelt by the Holy Spirit—the importance of, moment by moment, living according to the Spirit. How marvelous this is! But if, as we contemplate all of this, our hearts begin to fail us, how gentle is our God! How tenderly He picks us up and says, “Don’t you understand this is not to cause you to fear, it’s not to break your heart. It isn't to crush you to the earth. Quite the contrary, it’s to assure you that I have come to you and that I am your papa, your daddy.”
The word “Father” in this verse is the Greek word for father, while “Abba” is the Aramaic word for father. There is a very precious and a very important distinction between the two words. The Greek word “father” can be used like our English word “father.” It can have either a harsh or a gentle meaning. But the word “Abba” in the Aramaic is rather parallel to our word “Daddy.” It is a gentle term. Each language, surely, has a gentle word for “father,” which cannot have a harsh meaning. Paul wants us to understand the wonder and glory of being indwelt by the Holy Spirit. He wants us to do some heart searching as to whether or not we are living up to this highest of callings, this greatest of challenges. And yet at the same time, he wants to give us the greatest possible comfort. For the transcendent God of the universe is the one who in the stillness of the night, or when I have fallen in the mud, takes me by the hand and invites me to call Him Daddy.
From Chapter 11, "Life in the Spirit", in The Finished Work of Christ: The Truth of Romans 1-8, by Francis A. Schaeffer (Crossway Books, 1998)