Messiah means anointed one. This is a transliteration of a Hebrew word. The Greek word for it is Christ.
In the Old Testament (Hebrew bible) anointing was a ritual of pouring oil over someone who had been designated by God to fulfill an office. Three types of individuals were anointed: Prophets, Priests and Kings.
Jesus Christ, as Messiah, fulfills all three offices.
This chart summarizes the career of Messiah down through history, and the primary names and titles associated with him.
The office boundaries are not hard and fast, but given in the time period when that office is prominent.