She is both fearsome and benign, as are many Eastern deities of popularity and power. She appeals to the yogi and to the saint, in that She may be both horrid and compassionate, providing both a focus of meditation and a model for those of the Hindu Way who seek liberation (sometimes called 'moksha').
Kali-Ma is, to me, Mother Earth. She is a realistic, personal glimpse of natural power in humanoid form. While many favor one of Her aspects over the other (most notably and understandably the benign), those who cherish balance and broad-mindedness see and love Her in all Her manifested forms.
The stories of Her origins are often somewhat climactic. In one very popular story She is said to have been 'born' in a battle between the gods and the 'asuras', or titans. I would not call these forces 'evil' in the same way that some fundamentalist Christians might. The titans of Hindu mythos are necessary elements of the universal play ('lila') that the Cosmos - the myriad manifestation of Brahman (tao) makes possible.
Though Kali is associated with divinity, She has also been called 'Queen of the Demons' (and deservedly so). Her role could be compared to that of Persephone/Proserpine of the Greeks, who descends into the Underworld to rule there during half the seasonal and cosmologic cycle. Kali seems much more in control over Her destiny than the Greek goddess, however.
Let us begin, then, with this story to which I make mention (perhaps one of the first known concerning Kali):
The gods and the titans engaged in a great battle. There was one particular titan who was too powerful for the lesser gods to defeat. Durga, the Warrior/Mother goddess, was then called upon for aid. She arrived in splendour, riding a lion into battle, Her ten arms each bearing a magical weapon, Her...