Biblical Meaning: The name Abigail is a Biblical baby name. In Biblical the meaning of the name Abigail is: The father's joy. American Meaning: The name Abigail is an American baby name. In American the meaning of the name Abigail is: The father's joy.Hebrew Meaning: The name Abigail is a Hebrew baby name. In Hebrew the meaning of the name Abigail is: Father rejoiced, or father's joy.Gives joy.n American the meaning of the name Abigail is: The father's joy. Hebrew Meaning: The name Abigail is a Hebrew baby name. In Hebrew the meaning of the name Abigail is: Father rejoiced, or father's joy. Gives joy.