I am not very experienced in DSLR but I think I can speak newbie language (pros please don't mind me please).
Aperture (the opening that allows light to fall on the sensor aka "digital film") size is proportional to focal length divided by a number, i.e. f/#. In your case it is f/1.2 or 50/1.2. Since the # is the denominator, larger # means smaller opening.
If you remember the pinhole camera in primary school science, a bigger pinhole allows more light in, but things in the distance will be blurred. It is the same in a camera. A bigger aperture (your f/1.2 for example) allows more light in, thus reducing the time needed (high shutter speed, less prone to hand shake). But the tradeoff is a shallower depth of field. Meaning, the only sharp thing will be the person / object in focus. Other things like the background in the distance will be blurred.
Try taking pictures of the same object (with background in a distance) using different f/#. At f/1.2 the background will be very blur. Now switch your camera to Av and set the aperture to f/8.0. Take the same picture again. The background will be much clearer. But to allow the same amount of light to enter through the smaller opening, the shutter needs to be open longer. So if you try this at night you need a very steady hand so that camera shake will not affect your results.