All I know of Medusa is her hair was interpreted as snakes and she had the power to turn anyone who looked at her into stone.
With the help,of Wikipedia, I will try to explain Medusa's head.
Medusa, originally a beautiful young woman whose crowning glory was her magnificent long hair, was desired and courted by many suitors. Yet before she could be betrothed to a husband, Poseidon (Neptune) found her worshipping in the temple of Athena (Minerva) and ravished her.
Athena was outraged at her sacred temple being violated, and punished Medusa by turning her beautiful tresses into snakes and giving her the destructive power to turn anyone who looked directly at her into stone.
This is just a very very short version of her history.
Took this picture in Didyma (Didim) in Turkish