The official name for this hand brake is called the "E-Brake", which stands for Emergency brake. For manual transmission (and automatic also), you are supposed to leave your car in gear every time you park (or "P" for automatic). Sometimes on a steep hill, leaving your car in gear is not good enough, so the weight of the car is enough to get the engine to turn this letting the car start rolling. This is where your E-Brake comes in...it is your emergency brake (backup) that stops your car from just rolling away if something like that every happens. People refer to it as the hand brake as manual transmission drivers use it when they have come to a full stop on a hill and they want to start moving again (because the car will just roll backwards without the brake, and that is not good for the tranny and for the car behind you).
Also, you are NOT supposed to use the hand-brake when you are moving...it does not do anything and it will f*ck up your brakes!! When you are moving, the weight/intertia of the car is just way too much for the hand-brake...like I said, it only works when you are not moving.