So, Medusa was going out with Poseidon (God of the Sea) and Pioseidon, being one of the Big three, thought he was well head, and so he took Medusa on a date in one of Athena's temples. This was totally disrespectful in those days, and so Athena was not happy. So, she turned Medusa (and her sisters too, for good measure) into horrible creatures with snakes for hair and ugly faces, tails too apparently. Now, this is the foundation and fact (or what's written down in the History books, anyway) of my answer. For the true answer, I'm guessing that Athena gave them the power to turn anyone who made eye-contact into stone as a curse, so nobody could ever choose them again, even if they were looking through the horrible looks. Because they'd be statues.
She was given the power because she used to be this really beautiful mortal who was seeing posideon. He told her to meet him in Athena's temple. Athena said she was going to be a maiden forever so this was a HUGE offense. She then turned Medusa into a monster and did the same to her two sisters who helped her get into the temple.
Athena caught Poseidon raping one of her followers, Medusa, in her temple. Interestingly, Medusa was punished, not Poseidon. Athena turned Medusa and her sisters into Gorgons.
Turning people into stone
The Three Gorgons were the creatures that could turn people to stone.
Athena was angry because she caught Poseidon and his "girlfriend" Medusa in her temple; an offense of extreme disrespect. She then punished Medusa and her sisters by making them ugly and mean.
Medusa was one of the three "gorgons" their job was to turn people into stone.
They were turned into hideous creatures who have snake for hair and can turn people into stone with their gaze.
She is able to turn people to stone and is beautiful
Medusa, one of three gorgons. She could turn people to stone by making eye contact with them.
Medusa was a Gorgon. There were three Gorgons originally. Medusa had snakes for hair and as all Gorgons could turn men to stone.
Their names were Stheno, Medusa, and Euryale. And as a group they were the Gorgons.
There were three gorgons. There head looks weird and their hair is made of snakes. If you look at them you will turn to stone. The most powerful gorgon was Medusa.
In Greek mythology, after the two Gorgons, Stheno and Euryale, were killed by Perseus, Frank retrieved their heads from the river to use as weapons. These heads had the power to turn enemies into stone if they gazed upon them.