Leonardo da Vinci was a great painter. In fact he was great at a lot of things. He was probably a genius.
But he was not a magician. Even on NPR, when the topic is the Mona Lisa, some host will casually say how her eyes follow you no matter where you stand in the room. Can we all get over this?
When you paint someone on a two-dimensional surface and you paint their eyes pointing toward the viewer, the "eye-following" effect is created. Go ahead and try it out: Draw a smiley face on a piece of paper and look at it from the side. Or look at one of your family portrait photographs from JCPenny. If you're looking at the camera when the photo was taken, your eyes in the photograph will "follow" a viewer around the room.
Some paintings of mine even have this effect. And I'm not a genius. Or a magician.