When the right eye jumps or twitches, this is caused by strong nerve impulses traveling to the endings that supply the eyelid. According to WebMD, the most common cause of these involuntary spasms is overworking the eyes until they become strained or tired.
Another cause of eye jumps and twitches is the overuse of stimulants, such as caffeine, alcohol or street drugs. These substances over-stimulate the brain, causing it to send multiple and erratic messages along the nerve endings. Since the tissues of the eyelids are very thin, the spasms are more likely to be felt there than in larger masses of muscles.