I always understood the full phrase as "God speed the plough". So yes, this is a wish for prosperity and ease for whatever you're about to do. And we always shorten it to "godspeed". And Jura is very right to point out this is an old meaning of 'speed': success.
Apparently (after some research at the link below), the phrase comes from a 15th Century song sung by ploughmen on Plough Monday. That's the first Monday after the Christmas celebrations when they returned to work. Yes, I didn't know Plough Monday existed either. ;)
So the ploughmen would dress in white and drag a plough around the neighbourhood, asking for donations for drinking money. Probably to ease the experience of going back to work. :)
It may be interesting to look around this site to see what else they have:
www.phrases.org.uk/bulletin_board/31/messages/623.html
Oh yes - you use it to wish someone success when they are going to do something (work, or even travel). Although this has a very old-British feel. "I'm off to China, to negotiate a business contract." "Ok, godspeed!"