Abba (or Aba) means "father" in most Semitic languages. Most modern Israelis (along with other semitic-speaking peoples) call their fathers Abba as one would use "Dad" or "Daddy" in English.
Abba or Aba is the name of an important rabbi mentioned in the Talmud (a revered book in Judaism).
Abba—This Syriac or Chaldee word is found three times in the New Testament (Mark 14:36; Romans 8:15; Galatians 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 the English language. It has passed into European languages as an ecclesiastical term, "abbot." See Aramaic_of_Jesus#Abba
Abba is also the name of a brand of fish products sold in Scandinavia by the Swedish company Abba Seafood AB * The company dates back to 1838.