Galut or Golus (Hebrew: גלות), means literally exile. Galut or Golus classically refers to the exile of the Jewish people from the Land of Israel. There were altogether four such exiles.
Exile means to be away from one's home (i.e. city, state or country), while either being explicitly refused permission to return and/or being threatened by prison or death upon return. It can be a form of punishment.
Meshiach (Hebrew: משיח; mashiah, moshiah, mashiach, Messiah, or moshiach, ("anointed [one]") is a term used to describe Kohanim and kings, who were traditionally anointed with holy anointing oil as described in Exodus 30:22-25. But most-commonly, nowadays, it refers to The Moshiach, or מלך המשיח, who will redeem us from exile במהרה בימינו. אמן.