Blood is supplied to the brain by four arteries: The Carotid arteries and the Vertebral arteries.The Carotid Arteries run up the side of the neck and supply the Cerebral Hemispheres, and the Vertebral Arteries run alongside the spinal column and join together to form the Basilar Artery. The two Carotid Arteries and the Basilar Artery then join a circular artery called the Circle of Willis and this supplies the the brain with blood.
Cerebellar, like other types of strokes can be caused by either bleeding into the brain (haemorrhagic stroke) or, more commonly by the blockage of an artery leading to the brain (ischaemic stroke). The result of both types of stroke is a certain amount of brain damage.
Because the Cerebellum is responsible for balance and coordination the victim my have problems in these areas. For example walking may be difficult (or impossible) or the subject might stagger when walking (as if drunk!) due to the poor coordination. Because the body's balance organs also control eye movements, disruption of information to or from these organs may cause the eyes to have abnormal jerky movements either from side to side (horizontal) or up and down (vertical). This condition is known as Nystagmus.
Here is a diagram of the brain: