What does it mean when your left eye jumps?
Eye jumping, also known as eye twitching is a feeling that occurs either in the lower or upper eye, and which feels as movement on the eyelids. Different people have different beliefs over eye twitching. Some people believe that eye twitching means bad omen or ill luck ahead. See http://thankhealth.edublogs.org/2010/04/04/what-does-it-mean-when-your-eye-twitches-superstitionseye-twitching-superstition-is-true-or-false/.
If you mean a twitch in your eyelid, it's called a blepharospam. Basically harmless, though annoying. If it continues for an extended period of time (couple days or so) see a doctor.