What can be the reason for a twitching eye?

Nerve: Twitching eyes are usually caused by a nerve irritation. The nerve supplying the eyelids gets disturbed, usually temporarily, and reacts to it by firing that, in turn, causes one's eyelid to contract chaotically, causing what's known eye twitches. The condition in most cases is short lived and signifies no major abnormality.

Often unknown cause: Trembling of an eyelid, which happens in normal people, is called myokymia (an involuntary, spontaneous, quivering of a few muscle cell bundles within a muscle). Myokymia starts and stops spontaneously. In the eyelids, it can last a few minutes to a few days. One should see an ophthalmologist (md eye doctor) if such symptoms persist, keep recurring, or are combined with any other symptoms.

Myokymia: You are describing myokymia - an involuntary twitching of the skin around the eyelids. It's believed to be related to lack of sleep, stress, and caffeine use. Change these risk factors and it should abate.