The Collaborative International Dictionary of English v.0.48:

Abba \Ab"ba\ ([a^]b"b[.a]), n. [Syriac abb[=a] father. See
   Abbot.]
   Father; religious superior; -- in the Syriac, Coptic, and
   Ethiopic churches, a title given to the bishops, and by the
   bishops to the patriarch.
   [1913 Webster]

Easton's 1897 Bible Dictionary:

Abba
   This Syriac or Chaldee word is found three times in the New
   Testament (Mark 14:36; Rom. 8:15; Gal. 4:6), and in each case is
   followed by its Greek equivalent, which is translated "father."
   It is a term expressing warm affection and filial confidence. It
   has no perfect equivalent in our language. It has passed into
   European languages as an ecclesiastical term, "abbot."


Hitchcock's Bible Names Dictionary (late 1800's):

Abba, father