One famous Bible Commentator, Donald Guthrie had this to say about the term ABBA:
(Abba) was originally used by young children but it had acquired an extended meaning in familiar use roughly equivalent to "dear father".
It is a unique form that finds no parallel either in the OT or in Judaism, as an address to God.
Its use by Jesus shows how completely his view of God is divorced from any formal approach.
The "Abba" form conveys a sense of intimacy and familiarity which introduced an entirely new factor in man’s approach to God.” (New Testament Theology - D Guthrie)
From Martin Dale’s Sermon: The Lord’s Prayer