Literally it means to shoot, fire!
As slang: it means "say what's on your mind", "go ahead, say it!", "go ahead and start now" (when you are about to start doing something).
A :"I am really embarrassed to bring this up with you and I really don't know how to put it ...ehm......"( the person is literally squirming away trying to figure out the way to say it).
B: Don't worry, just fire away!"
2. "The contest is about to start. We have only two seconds: ...one.....two.....FIRE AWAY!!!"