Wikipedia describes Medusa as:

...one of the three monstrous Gorgons, generally described as winged human females with living venomous snakes in place of hair. Those who gazed into her eyes would turn to stone.

I can't remember specifically when I first encountered the myth of Medusa, but the earliest I can remember is seeing her depicted in the movie Clash of the Titans.  My mom loved that movie and whenever it showed on television, she and I would watch it together.  The thought of a character who was so beautiful that it was hard not to look at her, but so deadly that her gaze would petrify you and turn you to into a stone statue always fascinated me.  Painting her left me with a lot of idea.  Originally, her eyes were going to be left white, signifying the moment before you lose your life.  Then I considered painting them metallic, or with a mirror finish, but I eventually chose a strong gaze, giving the viewer that feeling like she is peering into your soul.