Generally, a black box is the term used to describe any system device or other object which contains information that can be viewed even if you don't know how it works (the idea is that the workings of the device can be opaque or black - in other words, you don't need to be able to see inside).
So the term has a very wide application, but most of us only hear it in connection with the black box on an aircraft. In this case it refers to the flight recorder (though in fact this is usually a bright orange to make it easy to find). The black box records everything said by the pilots and logs everything that is done with the controls and sensors. It also emits a signal for about a month after a plane crash, to make it easier to trace the aircraft, but even after this time has expired the recorded information is still extremely useful.