What is the name of the disease where eye ball trembles?

Nystagmus. Nystagmus is the medical descriptive term for what you describe. Nystagmus is not a disease. It is a descriptive medical term for an anatomic ocular manifestation. It can be horizontal, vertical or oscillatory. It is something that can be either congenital or acquired. If it is congenital, it is generally benign. If acquired, it could be a sign of a neurologic condition that needs work-up.