The cerebellum, also known as the "little brain" because it's folded into many lobes, lies above and behind the pons. As the second biggest area of the brain, it receives sensory input from the spinal cord, motor input from the cortex and basal ganglia, and position information from the vestibular system.
The "little brain" then integrates this information and influences outgoing motor pathways from the brain to coordinate movements. To demonstrate this, reach out and touch a point in front of you, such as the computer monitor -- your hand makes one smooth motion. If your cerebellum were damaged, that same motion would be very jerky, as your cortex initiated a series of small muscle contractions to home in on the target point. The cerebellum may also be involved in language (fine muscle contractions of the lips and larynx), as well as other cognitive functions.