The Jewish concept of messiah and the Christian concept of messiah differ. The Jewish view holds that a messiah is one chosen by God to do a specific work. Messiah is a word that comes from the Hebrew word "moshiach" (mo-shee-ock)which simly means 'the anointed one'. There there were in fact many messiahs according to the Jewish view.
In the Bible there are many accounts of there being a messiah. Before divine service to or for God, the person (chosen by God) was anointed with oil (a flask filled with olive oil was poured on the head of the person to be anointed). That was symbolic of the calling to and the equiping for the mission. For example, in the Book of Exodus 30:30 Aaron and his sons were anointed for service to God as priests. This is when the Levitical priesthood began. "You shall anoint Aaron and his sons and sactify (anoint) them to misister to Me.
(emphasis mine) In 1Samuel 9:16 Saul was anointed the first king over Israel. God told Samuel of Saul's coming arrival "You are to anoint him as prince over my people. He will save my people from the power of the Philistines..." In 2nd Samuel 2 David was anointed as king over Israel after David, his son Solomon.
According to the Jewish belief, the one spoken of in prophecy who will bring salvation to His people has still to come. The Christian concept of messiah differs in that the belief is that there is only one messiah, and that he HAS already come and is coming again.
Though their views differ, both Jew and Christian are awaiting the arrival of the one promised in many prophecies such as Isaiah 9:5 "For a child is born to us, a son is given to us;...