The cerebellum controls coordination. Damage to the cerebellum (whether from trauma, stoke or alcoholism) results in jerky movements, unsteady gait and a loss of grace.
A computing analogy for the geeks here: the cerebellum is sort of like the maths co-processor of the brain. Motor functions can occur without it, but are slower and not as fluid or smooth.
Gymnasts must have humoungously developed cerebellums, yes?