Get this: the bear was a sacred animal to Artemis. So most likely, the detail of Callisto's bear-y transformation is there because the she-bear is generally associated with the goddess. In some cults of Artemis, young girls used to actually dress up as bears as a part of certain rituals.
So before we go on, we'd just like to ask: if she really wanted to punish her, why didn't Artemis turn the nymph into a she-slug or something? Just saying.
At the end of the story, the she-bear, Callisto, and her son, Arcas, are transformed into the constellations Ursa Major and Ursa Minor (the big bear and little bear). Why? Have you ever wondered why people decided to make up these crazy stories about the constellations?
Well, back in the day, knowing your constellations was super important. If you knew what you were looking at, you could tell the time of night, year, and which direction you were going by the movement and placement of the stars.
The trouble is that when you first start scoping out the night sky, it looks like a big old mess of stars. Once you start dividing them up and grouping them, though, the whole sky reads like a book. Finding shapes and patterns in the stars is really useful for helping to remember what's up there. By connecting the dots into characters and making up stories to go along with them, it's way easier to remember what's going on in the night sky.
And there you have it: Ursa Major and Ursa Minor. P.S. In the States, we like to call them the Big and Little Dipper, but that's another story…