The Story of Mahisasura Mardhini

There is a legend for the reason behind her standing on what appears to be Shiva's corpse, which translates as follows:

Goddess Kali standing on Lord Shiva who lied on her path of rampage to stop Her.

There are many versions for this story. One of the version as follows:

There was a demon called Mahisa or Mahishasura who created chaos everywhere he goes.Goddess Durga, who had ten arms each carrying a weapon and who rode a lion or tiger in battle, fought with him. Durga became so enraged that her anger burst from her forehead in the form of Kali. Once born, the black goddess went wild and ate all the demons she came across, stringing their heads on a chain which she wore around her neck and Mahisa's head in her hand. She went on a raging rampage. No demon, human or God stood a chance at stopping her blood-lust. It seemed impossible to calm Kali’s bloody attacks, which now extended to any wrongdoers, and both people and gods were at a loss what to do. Fortunately, the mighty Shiva stopped Kali’s destructive rampage by lying down in her path, and when the goddess realised just who she was standing on, she finally calmed down.

In another version goddess Kali had destroyed all the demons in battle, she began a terrific dance out of the sheer joy of victory. All the worlds or lokas began to tremble and sway under the impact of her dance. So, at the request of all the Gods, Shiva himself asked her to desist from this behavior. However, she was too intoxicated to listen. Hence, Shiva lay like a corpse among the slain demons in order to absorb the shock of the dance into himself. When Kali eventually stepped upon Shiva, she realized she was trampling and hurting her husband and stopped and cooled down.

The Tantric interpretation of Kali standing on top of her husband is as follows:

The Shiv tattava (Divine Consciousness as Shiva) is inactive, while the Shakti tattava (Divine Energy as Kali) is active. Shiva and Kali represent Brahman, the Absolute pure consciousness which is beyond all names, forms and activities. Kali, on the other hand, represents the potential (and manifested) energy responsible for all names, forms and activities. She is his Shakti, or creative power, and is seen as the substance behind the entire content of all consciousness. She can never exist apart from Shiva or act independently of him, just as Shiva remains a mere corpse without Kali i.e., Shakti, all the matter/energy of the universe, is not distinct from Shiva, or Brahman, but is rather the dynamic power of Brahman. Hence, Kali is Para Brahman in the feminine and dynamic aspect while Shiva is the male aspect and static. She stands as the absolute basis for all life, energy and beneath her feet lies, Shiva, a metaphor for mass, which cannot retain its form without energy.

The simple explanation is that Shiva also known as Savam (corpse) and Kali known as Shakti (energy). is a metaphor for mas cannot retain its original form without energy. Soul (energy) is eternal and body (matter) is not permanant