'Shut' means 'close'. The 'front door' is the main door of a house or apartment. It is usually the door which leads directly onto the street or other public area. For example,if someone comes into your house without closing the door behind them, your front door is open. If you want someone to close it, you can tell them to 'shut' this door.

As Kevin posted on your discussion, it's a euphemism for "shut [the f***] up!" Nothing new here! :) Roger Daltrey of The Who sang "Why don't you all just f-f-f-(yes, go on Roger)-fade away" in the mid-sixties. Have you come across "see you next Tuesday" yet?

It means " shut your mouth up "