Kali makes her 'official' debut in the Devi-Mahatmya, where she is said to have emanated from the brow of Goddess Durga (slayer of demons) during one of the battles between the divine and anti-divine forces. Etymologically Durga's name means "Beyond Reach". She is thus an echo of the woman warrior's fierce virginal autonomy. In this context Kali is considered the 'forceful' form of the great goddess Durga.

Kali's fierce appearances have been the subject of extensive descriptions in several earlier and modern works. Though her fierce form is filled with awe- inspiring symbols, their real meaning is not what it first appears- they have equivocal significance:

A devotee poet says:

"Is Kali, my Divine Mother, of a black complexion?
She appears black because She is viewed from a distance;
but when intimately known She is no longer so.
The sky appears blue at a distance, but look at it close by
and you will find that it has no colour.
The water of the ocean looks blue at a distance,
but when you go near and take it in your hand,
you find that it is colourless."

... Ramakrishna Paramhansa (1836-86)

Kali's nudity has a similar meaning. In many instances she is described as garbed in space or sky clad. In her absolute, primordial nakedness she is free from all covering of illusion. She is Nature (Prakriti in Sanskrit), stripped of 'clothes'. It symbolizes that she is completely beyond name and form, completely beyond the illusory effects of maya (false consciousness). Her nudity is said to represent totally illumined consciousness, unaffected by maya. Kali is the bright fire of truth, which cannot be hidden by the clothes of ignorance. Such truth simply burns them away.

She is full-breasted; her motherhood is a ceaseless creation. Her disheveled hair forms a curtain of illusion, the fabric of space - time which organizes matter out of the chaotic sea of quantum-foam. Her garland of fifty human heads, each representing one of the fifty letters of the Sanskrit alphabet, symbolizes the repository of knowledge and wisdom. She wears a girdle of severed human hands- hands that are the principal instruments of work and so signify the action of karma. Thus the binding effects of this karma have been overcome, severed, as it were, by devotion to Kali. She has blessed the devotee by cutting him free from the cycle of karma. Her white teeth are symbolic of purity (Sans. Sattva), and her lolling tongue which is red dramatically depicts the fact that she consumes all things and denotes the act of tasting or enjoying what society regards as forbidden, i.e. her indiscriminate enjoyment of all the world's "flavors".

Kali's four arms represent the complete circle of creation and destruction, which is contained within her. She represents the inherent creative and destructive rhythms of the cosmos. Her right hands, making the mudras of "fear not" and conferring boons, represent the creative aspect of Kali, while the left hands, holding a bloodied sword and a severed head represent her destructive aspect. The bloodied sword and severed head symbolize the destruction of ignorance and the dawning of knowledge. The sword is the sword of knowledge, that cuts the knots of ignorance and destroys false consciousness (the severed head). Kali opens the gates of freedom with this sword, having cut the eight bonds that bind human beings. Finally her three eyes represent the sun, moon, and fire, with which she is able to observe the three modes of time: past, present and future. This attribute is also the origin of the name Kali, which is the feminine form of 'Kala', the Sanskrit term for Time.

Another symbolic but controversial aspect of Kali is her proximity to the cremation ground:

O Kali, Thou art fond of cremation grounds;
so I have turned my heart into one
That thou, a resident of cremation grounds,
may dance there unceasingly.
O Mother! I have no other fond desire in my heart;
fire of a funeral pyre is burning there;
O Mother! I have preserved the ashes of dead bodies all around
that Thou may come.
O Mother! Keeping Shiva, conqueror of Death, under Thy feet,
Come, dancing to the tune of music;
Prasada waits With his eyes closed

Kali's dwelling place, the cremation ground denotes a place where the five elements (Sanskrit: pancha mahabhuta) are dissolved. Kali dwells where dissolution takes place. In terms of devotion and worship, this denotes the dissolving of attachments, anger, lust, and other binding emotions, feelings, and ideas. The heart of the devotee is where this burning takes place, and it is in the heart that Kali dwells. The devotee makes her image in his heart and under her influence burns away all limitations and ignorance in the cremation fires. This inner cremation fire in the heart is the fire of knowledge, (Sanskrit: gyanagni), which Kali bestows.

The image of a recumbent Shiva lying under the feet of Kali represents Shiva as the passive potential of creation and Kali as his Shakti. The generic term Shakti denotes the Universal feminine creative principle and the energizing force behind all male divinity including Shiva. Shakti is known by the general name Devi, from the root 'div', meaning to shine. She is the Shining One, who is given different names in different places and in different appearances, as the symbol of the life-giving powers of the Universe. It is she that powers him. This Shakti is expressed as the i in Shiva's name. Without this i, Shiva becomes Shva, which in Sanskrit means a corpse. Thus suggesting that without his Shakti, Shiva is powerless or inert

Kali is a particularly appropriate image for conveying the idea of the world as the play of the gods. The spontaneous, effortless, dizzying creativity of the divine reflex is conveyed in her wild appearance. Insofar as kali is identified with the phenomenal world, she presents a picture of that world that underlies its ephemeral and unpredictable nature. In her mad dancing, disheveled hair, and eerie howl there is made present the hint of a world reeling, careening out of control. The world is created and destroyed in Kali's wild dancing, and the truth of redemption lies in man's awareness that he is invited to take part in that dance, to yield to the frenzied beat of the Mother's dance of life and death.

O Kali, my Mother full of Bliss! Enchantress of the almighty Shiva!
In Thy delirious joy Thou dancest, clapping Thy hands together!
Thou art the Mover of all that move, and we are but Thy helpless toys

...Ramakrishna Paramhans

Kali and her attendants dance to rhythms pounded out by Shiva (Lord of destruction) and his animal-headed attendants who dwell in the Himalayas. Associated with chaos and uncontrollable destruction, Kali's own retinue brandishes swords and holds aloft skull cups from which they drink the blood that intoxicates them. Kali, like Shiva, has a third eye, but in all other respects the two are distinguished from one another. In contrast to Shiva's sweet expression, plump body, and ash white complexion, dark kali's emaciated limbs, angular gestures, and fierce grimace convey a wild intensity. Her loose hair, skull garland, and tiger wrap whip around her body as she stomps and claps to the rhythm of the dance.

This terrific and poignant imagery starkly reveals the nature of Kali as the Divine Mother. Ramaprasad expresses his feelings thus:

Behold my Mother playing with Shiva,
lost in an ecstasy of joy!
Drunk with a draught of celestial wine,
She reels, and yet does not fall.
Erect She stands on Shiva's bosom,
and the earth Trembles under Her tread;
She and Her Lord are mad with frenzy,
casting Aside all fear and shame.

... Ramprasad (1718-75)

Kali's human and maternal qualities continue to define the goddess for most of her devotees to this day. In human relationships, the love between mother and child is usually considered the purest and strongest. In the same way, the love between the Mother Goddess and her human children is considered the closest and tenderest relationship with divinity. Accordingly, Kali's devotees form a particularly intimate and loving bond with her. But the devotee never forgets Kali's demonic, frightening aspects. He does not distort Kali's nature and the truths she reveals; he does not refuse to meditate on her terrifying features. He mentions these repeatedly in his songs but is never put off or repelled by them. Kali may be frightening, the mad, forgetful mistress of a world spinning out of control, but she is, after all, the Mother of all. As such, she must be accepted by her children- accepted in wonder and awe, perhaps, but accepted nevertheless. The poet in an intimate and lighter tone addresses the Mother thus:

O Kali! Why dost Thou roam about nude?
Art Thou not ashamed, Mother!
Garb and ornaments Thou hast none;
yet Thou Pridest in being King's daughter.
O Mother! Is it a virtue of Thy family that Thou
Placest thy feet on Thy husband?
Thou art nude; Thy husband is nude; you both roam cremation grounds.
O Mother! We are all ashamed of you; do put on thy garb.
Thou hast cast away Thy necklace of jewels, Mother,
And worn a garland of human heads.
Prasada says, "Mother! Thy fierce beauty has frightened
Thy nude consort.

... Ramaprasad

The soul that worships becomes always a little child: the soul that becomes a child finds God oftenest as mother. In a meditation before the Blessed Sacrament, some pen has written the exquisite assurance: "My child, you need not know much in order to please Me. Only Love Me dearly. Speak to me, as you would talk to your mother, if she had taken you in her arms."

Kali's boon is won when man confronts or accepts her and the realities she dramatically conveys to him. The image of Kali, in a variety of ways, teaches man that pain, sorrow, decay, death, and destruction are not to be overcome or conquered by denying them or explaining them away. Pain and sorrow are woven into the texture of man's life so thoroughly that to deny them is ultimately futile. For man to realize the fullness of his being, for man to exploit his potential as a human being, he must finally accept this dimension of existence. Kali's boon is freedom, the freedom of the child to revel in the moment, and it is won only after confrontation or acceptance of death. To ignore death, to pretend that one is physically immortal, to pretend that one's ego is the center of things, is to provoke Kali's mocking laughter. To confront or accept death, on the contrary, is to realize a mode of being that can delight and revel in the play of the gods. To accept one's mortality is to be able to let go, to be able to sing, dance, and shout. Kali is Mother to her devotees not because she protects them from the way things really are but because she reveals to them their mortality and thus releases them to act fully and freely, releases them from the incredible, binding web of "adult" pretense, practicality, and rationality.

http://www.hindupaintings.com/article/kali