It means you spend all of your time making money, get good grades, earning awards, things of that nature, and you do not take time to relax, have fun, spend time with your family. It is not always a negative thing, but it does carry the connotation that the person may be overly stressed or a bit of a bore.
An over-achiever can be a student who gets all As in school and is in many clubs or it can be a professional who works 80 hours a week.