Shiva is half woman God or Ardharnareshwar (ardha-nari-ishwar). This image is often assumed to represent gender equality. But the male and female halves of the image have less to do with the reality of gender and more to do with the representation of gender-neutral ideas.
God, in Hindu mythology, represents human imagination that can be worshipped (independent Shiva, dependable Vishnu) or not worshipped (dependent Brahma) while Goddess represents nature. Human imagination needs nature but nature does not need human imagination. Hence God becomes half the Goddess but the Goddess never becomes half a God.
These definitions of God and Goddess are unique to Hindu traditions, and not found in other parts of the world. They are often confused with biblical notions of God, which is an external agency outside humanity and nature.
Of course, despite all attempts to communicate metaphysical ideas through such imagery, people remain oblivious to them and prefer stories, which can often be taken literally and very simplistically. But such stories allow for its transmission over generations. Compared to the images, stories of Ardhanareshwara are relatively rare. Below are a few retellings.
According to Linga Puran, in the beginning, a lotus bloomed. In it sat Brahma. On becoming conscious, he realized he was alone. Lonely, frightened, he wondered how he could create another being to give him company. Suddenly a vision flashed before his eyes. He saw Shiva whose right half was male and left half was female. Inspired, Brahma divided himself into two. From the right half came all things male and from the left half came all things female.
In the oral tradition of Nath Jogis it is said that sages who visited Mount Kailas were at first horrified to find Shiva in an intimate embrace with his consort disregarding their presence. Then they realized that for Shiva to stop and pull back would be like asking the right half of the body to separate from the left half. So they saluted Shiva and visualized him as the half-woman god.
Tamil temple lore tells us about Bhringi who wanted to circumambulate Shiva but not Parvati. Parvati would not allow that. She sat on Shiva’s lap making it impossible for the ascetic to pass between them. When Bhringi took the form of a bee to fly between their heads, she merged herself with Shiva so that she became his left half. Now Bhringi took the form of a worm and tried to bore his way between them. Parvati was not amused.
She cursed Bhringi to lose every part of the body given to him by his mother. As a result, the ascetic was left with neither flesh nor blood (the soft parts of his body). Reduced to a skeleton he could not stand upright. Taking pity on him Shiva gave him a third leg so that he stood like a tripod, reminding all of the price man pays if he does not revere the feminine half of the divine.
A folk tale from the hills of North India tells us that when Parvati saw Ganga on top of Shiva’s head, she was furious. How could he keep another woman on his head when his wife sat on his lap, she wondered. To pacify Parvati, Shiva merged his body with hers. He became half a woman.