On my oven broil is top heating element only, bake is bottom only. Some ovens use both to speed up initial heating time and then only use one element.
The broil setting is good for steaks and stuff that needs direct heat. Put the oven rack near the top and broil away. Also can be used to brown stuff like pizza cheese, or even make toast.
The bake setting is for indirect heat like cakes, pies, etc.