The story goes this way. She had a lover (a fiance) whom she lost, and this devastated her so much that she was no longer prepared for the great art modelling she had signed for. This was a noble art commissioned by a very influencial figure, so Leonardo Da vinci had to hire jesters to perform to make her happy. At a point, the jesters did something amusing, that made her to smile. Though smiling, Leonardo da vinci succeed in capturing her momentary joy and long time sorrow.
This was the exact impression that made the portrait very popular and also for the fact that there are two eye levels at the back ground of the portrait.