Answer:
Medusa is one of the Three Gorgons, sister of Stheno and Euryale. While they are all hideously ugly, Medusa is the only one among them with the power to petrify people with her gaze.
Storyline Behind Her:
Medusa was a daughter of Phorcys and Keto, and was once a priestess of Athena. Poseidon was bitter at Athena for recently turning his beloved Koroneis into a raven, so he decided to get back at her by becoming obsessed with the beautiful girl. Despite being warned about sea gods by her sisters, she was actually flattered that Poseidon liked her. He took her to a town's temple for Athena. As a result of the two getting romantic at the foot of the statue of her, the infuriated and disgusted Athena cursed Medusa, much to Poseidon's horror and dismay. The girl's hair was turned into serpents and any mortal who would look upon her gaze would turn to stone. Eventually, she ended up living in a cave far from civilization with just her sisters, Stheno and Euryale, the three were called the Gorgons. Medusa's sisters were eventually made immortal, though they do not have the power to turn people to stone like her.
Medusa had two children with Poseidon, Chrysaor, who was born from her neck, and another child, Pegasus. At first, these two children were trapped inside her after she was turned into a monster but were later born from her blood when Perseus beheaded her while the Gorgon was asleep. The hero would subsequently use Medusa's severed head to defeat Poseidon's ferocious sea monster saving his future wife, Andromeda, in the process. (Sorry for all bold I didn't mean to lol)