Kali is the female form of Kala or Time. She is the origin and the end. Her four arms mean absolute dominion over all that the world contains. Her necklace of skulls signifies that she supports the living and the dead. Her colouring is dark, signifying the ultimate energy into which all things disappear. Her terrifying image shows that she herself is without fear and thus can protect her worshippers from fear.
Like Shiva, she frequents lonely places like the outskirts of towns and even cremation grounds. In some myths, she is supposed to be the anger of Durga as she killed the demon Mahishasura.
But the most popular myth depicts her as the killer of the demon Raktabija. Some scholars say that Parvati took on the form of Kali to help her son Skanda in battle. In the war with Mahishasura, each drop of blood from the evil Raktabija produced new demons, Kali, dark as death, spread her tongue over the battlefield and licked the demon’s falling blood before it could touch the ground. So new demons could not be spawned, enabling Skanda to attack and kill Raktabija with ease. Intoxicated by the blood, Kali ran amuck across the three worlds destroying all in her path. To restrain her, Shiva took the form of a corpse and blocked her path. When Kali found herself standing over her husband, she was jolted out of her frenzy. She wondered of she had killed her own husband and placed her foot on his chest and brought him back to life. This story demonstrates that both are necessary to save the world from destruction — the male with his inertness and the female with her shakti.
Another account says that she sprang, in full armour, from the eye of Durga and joined her in destroying the powers of darkness.
SOURCES: Gods and Goddesses of India by Anjula Bedi, Devi, The Mother Goddess -An Introduction by Devdutt Pattanaik.