Something fierce seems wild, strong, and dangerous. A fierce dog looks angry and ferocious, ready to attack. A fierce storm is loud and powerful, able to drown a boat at sea by stirring up the choppy water or set a tree on fire by striking it with lightning.
You don't have to be big or bad to be fierce. A hungry baby has a fierce cry: loud, forceful, and painful to hear. If you're about to do something that scares you, like ride a rollercoaster or get a shot, you might keep a fierce grip on your mom's hand: a strong, tight grip. Even a fight, an argument, a performance, or a competition can be fierce if people are being loud, strong, powerful, and impressive.