Eyelids twitching is a repetitive involuntary spasm of the eyelids. Although the actual cause is unknown, there are certain factors that may lead to this spasm like fatigue, eye irritation, physical exertion, caffeine, alcohol.
It usually mild,painless and goes away in a few days so you have less to worry about. Only when it gets severe and twitching could be strong making both eyelids shut. This is a condition called "blepharospasm". You might consider a doctor for that.