Artemis, the goddess of the hunt and the moon, was always accompanied on her adventures by a band of nymphs. One day the nymph Callisto asked to join her. After taking the oath of chastity required by Artemis of all her followers, Callisto was allowed to join her.
One day Zeus, the king of the gods, came across Callisto as she lay asleep. He fell in love with her, overpowered her, and gave her a son Arcas.
Both Hera and Artemis were furious with Callisto. Hera because of Zeus's adultery, and Artemis because she had violated her oath of chastity. To protect Callisto, Zeus concealed her by changing her into a bear. For many miserable years she wandered the forest, pursued by the very huntresses who had once been her companions.
One day Arcas, who had grown up to be a great hunter, saw his mother, without recognizing her in her bear shape. He drew an arrow to slay her, but at the last moment Zeus turned him also into a bear, and transported them both into the sky as the constellations Great (Callisto) and Little (Arcas) Bears.
Hera was angered by the honor paid to her rival, and persuaded Poseidon to not let her bathe in the ocean's waters. That is why the Great Bear is always in the sky. However, this injunction was relaxed, and the Great Bear in fact dips slightly below the horizon.
There in the sky Callisto and Arcas will live forever.