Biblical Jewish Aramaic unlike Biblical Aramaic is the Aramaic used in the Babylonian Talmud and religious academies in Babylon.
Biblical Jewish Aramaic is indespensable if one wishes to understand the oral law (as preserved in the Talmud) and therefore the literature, rules, mind-set and thought patterns of the Jews. Jesus encountered the doctors of the law, the scribes and the Pharisees.
He also showed a tremendous familiarity with the oral law, the rules of exegesis and protocols found in the culture and was thus able to contextualize his message in a manner which could appeal to the hearers and bring understanding.