Aramaic is a semitic language - or, technically, a whole family of related languages, rather like the different dialects of Chinese. Various forms of it were spoken throughout the Middle East from early antiquity onwards, and some are still spoken today. Parts of the Old Testament were written in one form of it, although most of the OT was of course written in Hebrew. Several different dialects made up the everyday language of Palestine in Jesus' day. Hebrew, a largely unrelated language spoken by the Jews, was also still spoken at this time, and would continue to be spoken in Palestine for another couple of centuries before largely dying out other than as a literary language (the Hebrew spoken in Israel today is a modern resuscitation of the language). But no-one knows exactly what roles Hebrew and Aramaic played during this period, especially given the extra complication of Greek, the official Roman language, which was extensively spoken in the cities. It would not have been uncommon for a Palestinian Jew in Jesus' day to speak Greek, although obviously the more educated you were and the bigger the city you lived in, the more likely you were to speak it. The variant of Aramaic called Syriac - which was spoken in Edessa, the first officially Christian city - became the standard language of Christianity in the Middle East for centuries.