When you became a child of God by accepting Jesus Christ as your Lord and Savior, the Holy Spirit came to dwell in you. The Bible says in Rom 8:15 that we did not receive a spirit of bondage rather we received the Spirit of adoption. In other words when you were an unbeliever your life was dominated by the spirit of bondage which caused you to be bound in sin and fear.
The word adoption in Rom 8:15 refers to your engraftment into God's family. You were a stranger to God's family, and a slave to sin previously but by identifying with Christ you became a child of God, adopted into the family with all the full rights and privileges of the 1st Son, Jesus Christ.
When you became a son of God your past was wiped away and it was as though you were always a son. Now, you can confidently approach the Father with boldness because of your status as a child of God. This why you can use the affectionate term Abba, and say Abba Father.