The Messiah in Judaism means anointed one; it included Jewish priests, prophets and kings such as David and Cyrus the Great.
[1] Later, especially after the failure of the Hasmonean Kingdom (37 BCE) and the Jewish–Roman wars (66–135 CE), the figure of the Jewish Messiah was one who would deliver the Jews from oppression and usher in an Olam HaBa ("world to come"), the Messianic Age.
Others, like the author of the Psalms of Solomon, stated that the Messiah was a charismatic teacher who would give the correct interpretation of Mosaic law, restore the monarchy of Israel, and judge mankind.
Claimants who emerged in the early part of the 8th century in Persia included: Under the influence of the Crusades the number of Jewish Messiah claimants increased, and the 12th century records many of them; I shall reveal to you in this matter what has been buried and hidden in my heart forever, ... and I have never revealed it to anyone ... except for my father-in-law and my grandfather-in-law, may their souls rest in peace [these are "The Old Rabbi," Rabbi Shneur Zalman of Lyady, and his son the middle rebbe]: and this is that our fellows.. .
do not know and are unable to estimate the value and the great benefit and great grace that the Vilna Gaon did for us in disagreeing with us.... Because were it not for that controversy, there would have been reason and place to worry and fear that the new system that we paved for ourselves ... would slowly lead us, step-by-step, forward beyond the border meant for the Torah heritage and the commandments.... For by virtue of the power of enthusiasm and fervor of the soul and elevation of spirit in the course of the new system that gripped the hearts of its creators in a storm,.. .