Anointed One, or Hebrew Messiah. Based on the Hebrew mashiach, or "anointed for God's purpose". Plainly, the anointed one was set aside before God and for God for His will. In its adjective form, this word was applied to both priests and kings of the Old Testament, or Tanach.
Its use as a noun however, and the form of Messiah and Christ that is now used, begins in the New Testament, referring to the Anointed One of God, a single person who was sent to fulfill Old Testament prophecy. This title was applied to Jesus of Nazareth both during His life and after His death and ressurection. (Note: During His life He was generally referred to as Messiah by the Jewish crowds He spoke to, but after Greeks and other Gentiles became involved, the translation Christ became more popular.)
In particular, the title of Christ, or Anointed One, was a way of recognizing one someone set apart by God. It was applied to Jesus not as a specific title, but as an affirmation that He was the One whom God promised throughout the Tanach.