There are a couple of movies I heard actors using Godspeed as a way to say goodbye. At least I interpreted it this way. I though never heard anyone use this expression in the UK, Ireland, Australia, U.S. or Canada. Is this really a common expression? Does Godspeed have anything to do with the speed of god? Originated from religion?
Godspeed is an archaic way of saying goodbye, and is used in modern English in situations where very great earnestness is not inappropriate, such as a very dangerous mission, for example, where lives are at risk.
It means "May God speed you", that is, may God give you success. It is a wish for a safe, successful outcome.
P.S. If the situation is not at all serious or dangerous, and someone says "Godspeed", the word is being used in a jocular, mocking, or ironic manner, making something more of the situation than it really is, or to indicate that someone else is making more of the situation than it really is.