It means to not give oneself enough credit, or to be overly humble. For instance, if you are a fantastic pianist, someone asks you if you play any musical instruments and you say "Oh, I can play the piano a little bit", you are "selling yourself short"! You have underplayed your talents.
People are sometimes guilty of this when writing their CV/resumé. In order for a CV to really grab the attention of a potential employer, you have to really sell yourself!! If you are too modest about your abilities, then you may be overlooked for a job. So if you don't really make yourself sound amazing and perfect for the job, you have "sold yourself short".
I think it originates in the stock market where I believe "short selling" is a practice, but I have no idea what it means!