Do you mean the actual eyeball, or the eyelids or surrounding areas?

Several superstitions surround twitches in the left eye, which can be considered a good or bad omen depending on the culture. The area of the eye which is twitching and the gender of the person experiencing this symptom will also play a role in the superstition. In Chinese culture, a twitch in the left eye is said to signal good fortune for men, but a sign of misfortune for women. In Indian culture, this belief is reversed. If the lower lid is twitching, the Chinese believe this is a sign that someone may be gossiping about you. Hawaiians believe that a twitch in the left eye signals that a stranger will arrive soon, and constant twitching forewarns the family of imminent demise. Some African cultures also believe that your lower eye twitching means you will meet someone unexpectedly or you will soon shed tears of sorrow.

Medically speaking, it is not the eye that twitches but rather the muscles in the eyelids having spasms which cause this strange sensation. This will lead to a strange fluttering around the eyes which can be uncomfortable or cause a temporary disturbance in your vision. Sudden eye twitches are often temporary and can easily be relieved. If your eye twitches regularly or severely it can be a sign that you have an underlying condition which may require treatment

http://www.md-health.com/Left-Eye-Twitching.html

Eye strain... or can sometimes happen if you're under stress.