Shiva doesn't exist without Shakthi. Shiva and shakthi are one. I recently visited a temple of Mother Kali. I was purplexed to see lord shiva in a smiling face is under the feet of angry Mother Kali. What does this signify?
Swami Paramhansa Yogananda says in Paramhansa Yogananda, from The Essence of Self-Realization, Ways in Which God Can be Worshiped:
Kali represents Mother Nature. She is Aum, the cosmic vibration. In Aum everything exists—all matter, all energy, and the thoughts of all conscious beings. Hence, Her garland of heads, to show that She is invisibly present in all minds.
The play of life and death expresses Her activity in Nature: creation, preservation, and destruction. Hence the sword, the head, and a third hand extended, bestowing life.
“Her energy is omnipresent; hence Her streaming hair, representing energy.
Shiva, Her husband, represents God in His vibrationless state, beyond creation. Thus, He is depicted as supine.
Basically that Kali being the Shakti, creates, preserves and liberates the Universe. All this She does on behalf (because they are both One) of Lord Shiva, who is the vibrationless, Nirguna Brahman, motionless, undescribable, bliss and without attributes. Thus Shiva lays motionless and smiling in bliss, while God Kali performs the acts on His behalf.
Sri Ramakrishna Paramhansa says in The Gospel of Sri Ramakrishna – (page 271 – 2):
Whatever you perceive in the universe is the outcome of the union of Purusha and Prakriti. Take the image of Shiva and Kali.
Kali stands on the bosom of Shiva; Shiva lies under Her feet like a corpse; Kali looks at Shiva. All this denotes the union of Purusha and Prakriti.
Purusha is inactive; therefore Shiva lies on the ground like a corpse.
Prakriti performs all Her activities in conjunction with Purusha. Thus She creates, preserves, and destroys.
Thus Kali represents the vibration or Aum which is responsible for creation, preservation and liberation, while Shiva is the absolute.
This does not mean that Kali is not Nirguna or that Lord Shiva is not Saguna. This is the symbolism with which one can understand this particular depiction of the Gods. Each depiction can have multiple interpretations and multiple meanings. All Gods are One. The one manifests itself in various forms.
Ekam sat vipra bahudha vadanti (Rig Veda (1.164.46))
The Reality (Truth) is one: the wise call It by various names.
Sarvam khalvidam brahma. (Chandogya Upanishad 3.14.1)
All this is Brahman
The story is like that once upon a time Devi Kali got very angry from devils and start killing everyone. No one was able stop her who is source of energy and power. Only Lord Shiva knows how to stop her. He is husband of Devi Shakti and Devi Kali is a form of Devi Shakti so she would also behave like a wife of Lord Shiva. Lord Shiva lay down on the way of Devi kali and once she putted her feet on him realize that its totally wrong and she went calm.
I am quoting this from my article-
"She is usually depicted as having one of her legs on the chest of Lord Shiva who lies on the ground in a static state. This represents the Purusha-Prakriti aspect of Samkhya. Shiva is static absolute Brahman, Kali is the power of this Brahman to have motion. Therefore, Shiva is lying without movement and Kali is standing or dancing on him.
In some depictions, especially with respect to forms like Chinnamasta, the Shakti is shown as being in a sexual union with Shiva who is lying static on the ground. The imagery is a direct depiction of the cosmic union of Purusha and Prakriti. The fact that Brahman and his power are non-different is being depicted in this imagery. The sexual union being the physical imitation of the cosmic union, the imagery aims to highlight the comic and spiritual union through sexual union. Further, in certain tantrika sadhanas (tantrika practices), the sexual energy is used to attain a spiritual union."
You can read the whole article here- "Why the West does not understand Kali"-http://www.newsgram.com/22503/
I was purplexed to see lord shiva in a smiling face is under the feet of angry Mother Kali. What does this signify?
First, I would like to point out that Sai's answer is in a sense incomplete because Kali with an angry face doesn't seem to symbolize Shakthi (though Shiva lying on the ground like a corpse matches Nirguna Brahman). Yet, this doesn't rule out that interpretation.
I shall give a wikipedia reference here: Kali (see the references therein; feel free to add references here and in the wikipedia article).
Note that there are two types of "Shiva under the feet of Kali" poses. The one OP is asking about is of Vamakali. The other one is of Dakshinakali (see the section Dakshinakali in the wikipedia page for Kali).
Dakshinakali's two right hands are usually depicted in gestures of blessing(abhaya mudra) and giving of boons(varada mudra), and is typically shown with her right foot on Shiva's chest. Her two left hands holds a weapon and a severed head. Sai's answer matches well with the image of Dakshinakali. In this image, Dakshinakali is indeed the picture of Shakthi. But in this depiction Kali is not angry. Though, the Goddess is still fearsome, there is at least a hint of mercy on the face, (yet her red tongue is out).
There is an interpretation that Shiva was attempting to receive Kali's grace by receiving her foot on his chest (This might be an interpretation of devotees for the story of Kali's dance of death and Shiva stopping it(?) by lying on her feet).
On the other hand, Vamakali or Samharakali is the very embodiment of anger (in some interpretations the anger of Durga). She is depicted in a fury, and with her left foot on Shiva's chest. This pose shows the conclusion of an episode in which Kali was rampaging out of control after destroying many asuras (raktabiija and his consrots). Kali had a unstoppable frenzied dance of destruction. Shiva, fearing that Kali would not stop until she destroyed the world, could only think of one way to pacify her. He lay down on the battlefield so that she would have to step on him. Seeing her consort under her foot, Kali realized that she had gone too far, and calmed down. It is this story that Kenneth pointed out in his answer.
Addendum: There are some sources (not widely accepted i think) which supports only the first interpretation (that Shiva is taking blessing from Kali). These sources are Yogini Tantra and Kalika Purana. (See this for more precise pointers). According to these sources, Shiva got a boon from Mother Goddess (Mahakali) that he can have a place below her feet. For this, Shiva took the Asur incarnation of Mahishasur to be killed by Kali, and thus take a permanent position at her feet.
One take away from all this (not just that in addendum) is that not only kind forms but also also fearsome and/or cruel forms are that of God.
One day the demon Raktbeej was fighting with the Gods with his armies. The Gods were can't fight with Raktbeej. Goddess Parvati was very angry and she was transformed into her incarnation Kali. Goddess Kali was the Goddess of ghosts. Raktbeej was fighting with Kali. She was trying to kill Raktbeej with her weapon but when Raktbeej's blood was falling,it was transformed into another Raktbeej. Kali was eating Raktbeej's blood. She was too much angry and she was also trying to destroy the Earth. Kali killed Raktbeej and she was wearing many Raktbeej's heads. Suddenly Kali saw she was standing on Lord Shiva his husband. She opened her tongue because she was standing on her husband and also she was feeling shame. Kali became calm and she was transformed into Goddess Parvati.