What does it means when the left side of your face hurts bad?

Facial pain. The answer depends on many variable factors. Possibilities include a migraine headache, sinus or ear infection, or tooth related pain. If the pain lasts over a day; or has increased in frequency, you should be examined by a health professional.
See someone. It means that your body is telling you that somethings is wrong in that area. I would see my dentist first. Do it now that is serious.