To twitch is to make a very sudden, brief, unintentional movement. Your eye muscles might start to twitch when you're extremely tired.
Back in the 12th century, instead of using the word twitch, you would've used to-twic-chen, which was defined as "pulling apart with a quick jerk." It stemmed from the Old English twiccian, "to pluck, gather, or catch hold of." Today, we use twitch as a noun too, to mean the jerky spasm itself: "She tried not to laugh, but he could see a twitch in her lip."