(inset obligatory reference to the movie "Face/Off" here. You might as well get it out of your system.)
A security feature found on many Car Stereos made in the last decade or so, formerly on higher-priced and higher-end devices, but that have steadily made their way down the lines to the more "budget" oriented lines as well.
The concept is simple -- the front of the unit, where all the user controls are located, is actually an easily removable panel that when removed leaves the rest of the system unable to operate and thus makes is a less tempting target for a thief.
There are, in broad terms, two types of detachable faces. The first and most common is the electronic face, in which the buttons and control on the plate are electronic switches and are connected to the rest of the system through an electrical connector; the visual display parts of the system will also be usually built in to the faceplate as well so when removed the only visible marks on the remaining (in car) portion will be the electrical connection and perhaps the media slot (e.g. CD or Tape).
The second kind, an altogether rarer and more primitive style, is the mechanical variety in which the switches on the face plate are merely spring-loaded rods that push through the face plate and actuate smaller controls on the other side. In this style the LCD/VFD display will be fixed permanently to the stereo and so removal of the face will remove the buttons but not the LCD, and there will still be blank switch holes on the exposed face. The upside of these is that they are cheaper to produce and since they are not electrical that are not as fragile.
Their history is scant, but in the researched I've done I've been lead to believe that Pioneer was the first company to offer a detachable face on it's first or second CD playing head unit, circa 1991. Blaupunkt and Kenwood got in the act soon after and Sony was the late-commer. Now it's rare to find a high-end stereo that doesn't have a detachable, flip-around or featureless face.
But do they work? That's really a debated question. The reason they are supposed to work is because to buy a new face for your stereo will cost a lot more money then a thief is willing to commit to any enterprise. They also could assumably dissuade a crook from breaking into the car and stealing anything else while he was there. My opinion is that a functionless stereo is no-good to a thief and so my detachable face gives me a little extra comfort when I'm parked in the bad part of town.
This is in no way a reference to the detachable penis. You sickos.