Callisto is a Greek Nymph, that is an attendent of the goddess, Artemis. This means that she is a follower of Artemis, which means that she had to take a vow of chasity
Zeus fell in love with Callisto. He disguised himself as Artemis and had his way with her against her will, which made her pregnant with his child.
Callisto had Zeus' child and named him Arcas. Shortly after she gave birth to her son, Callisto was transformed into a bear by Hera, who was extremely jealous of her and Zeus. Once Callisto was a bear the god Hermes to Arcas to Maia to raise him.
Hera was still not satisfied after turning Callisto into a bear, so she tried to persuade Artemis into believing that Callisto was an actual bear. Zeus saw what Hera was doing and he saved Callisto by turning her into the constellation Arctos, the Great Bear, also known as Ursa Major.
After a little while of Maia and Hermes raising Arcas, he finally joined his mother as the constellation Arctophlayx, the Little Bear, also known as Ursa Minor. (I think you can see the connection there).
Hera, even after all this time, was still not satisfied, so she talked to Tethys and Oceanus, and got them to forbid Callisto from entering their realm, the ocean. From know on Callisto must always circle the Northern Star and never set over the horizon.