First of all, the following, like most endeavors into history, is entirely speculation since we cannot eat Leonardo da Vinci's brain to gain his knowledge
The true identity of the subject of the Mona Lisa painting is not known for certain. No one knows for sure who it was because the work was never signed or titled by Leonardo da Vinci. Neither have there ever been records found indicating the work had been contracted. The title "Mona Lisa" was given to the painting by an early biographer (whose name escapes me, it may have been Giorgio Vasari) of da Vinci, who based the name on the memories of some old French man who had been only a child in da Vinci's time, and foggily remembered hearing da Vinci had named Lisa Gherardini de Giocondo as his painting subject.
The other popular theory is that this is a painting by memory of Leonardo's mother, of whom he was fond, despite being raised by his father. The background of the Mona Lisa is supposedly that of Leonardo's home town of Vinci (Leonardo da Vinci = Leonardo of/from Vinci). Leonardo was also big on word games: one example (this may be wrong) would be his portrait of Ginevra de Benci, whose name means juniper in Italian, had a background of juniper trees. The same idea may apply to the Mona Lisa, with the background of Vinci identifying its subject.
Also the pattern on Mona Lisa's bodice was very unusual for it's time. It is a style known as "knotwork". The word for knotwork in Italian is vincire. Again the wordplay implies the name Vinci.
These two facts coupled together make just as good an argument for the subject as Da Vinci's biographer. Again both theories are speculation, neither can be proven (or my Art History II professor likes to make up stories).
Another theory is that the painting was of Leonardo himself, as a woman. Apparently if you mirror his self-portrait onto that of the Mona Lisa, the features match up.