The Cerebrum is the right and left hemispheres of the brain. Each hemisphere contains four lobes. The Frontal, the Parietal, the Occipital, and the Temporal. These lobes are what control functions like vision, memory, hearing, etc.
The Cerebellum is known as the "Little brain" in Latin (literally means that). This is the part of the brain that controls motor activity, as well as helps a human maintain it's posture and balance. This also is what controls a human beings ability to perform rapid movements, such as running, dancing, etc.
Your Brainstem is simple. It helps everything that you do unconsciously, such as bodily functions. Examples little things!! (sarcasm): Breathing, digestion, pulse, etc.