Using the neurological examination to test coordination primarily assesses cerebellar function.
The cerebellum is important for motor learning and timing of motor activity. It fine-tunes agonist and antagonistic forces of muscle activity, simultaneously and sequentially, across multiple joints which results in smooth and purposeful movements.
Cerebellar dysfunction causes deterioration of movements, with subsequent under-shooting and over-shooting of purposeful movement, also known as dysmetria.
Deterioration of movement and dysmetria are precursors to the development ofataxia.