A metaphor for: "I think you should leave. Do not pause or delay while you are leaving." Generally used when the addressed has been complaining about circumstances that the listener doesn't agree with. It comes from a time when doors were on spring hinges and if you paused in the doorway while exiting, the door would spring closed behind you and hit you on the backside.
"This place stinks. I am too qualified to be here."
"Well, don't let the door hit you on the way out."