Ardhanishwar is one of the very important form of God, Hindus worship. In the form of male and female, mazy hair with moon, axe, smeared in red (aruna), wearing snakes and the skin of tiger, embracing the bull and with a bent leg, this the right half, and the left black in color, hand holding a lily flower, with a silk like lotus foot, wearing gold ornaments represent the rest half female God.

We do not say that the God is only male. God is male- female and neuter too. A concept of God is beyond gender. It is we human who make a difference in every aspect whether it is on caste basis or on gender basis. Ardhanishwar is an incarnation of shiv and his Shakti to signify that without women this world is not but a nirgun Brahman, similarly without Shakti, shiv is nothing i.e. Lord Shiv’s illusive power is shakti.

There is a story behind the personification of Ardhanishwar:-

Sage bRingi is one of the zealous devotees of Lord Shiva. He used to worship only Lord Shiva and not Shakti. Goddess Shakti, being the power pulled out the energy from bRingi mahaRishi's body. And he was even unable to stand. He pleaded to God. Lord Shiva provided him with a stick. On its support he stood and still worshipped Lord Shiva alone. Goddess Shakti wanted to become an inseparable part of Lord Shiva's form. She observed the kEdhAra mahA vrata (1) penance which is now known as deepAvaLi. Pleased with her austerity, Lord Shiva granted her the boon of being part of His form. So the Lord now appeared male on the right side and female on the left side and hence became ardhanArIshvara.

Purna of the deity ardha nAri Ishvarar i.e. half female God (bhOga mUrti)

According to the Hindu mythology, this form is quite associated with the Grace of God. Shiva and Shakti are one and the same Supreme. The formless God is called parashiva. On Its own free-will for the benefit of souls, which are drowned in bondage, it thinks to create the worlds. The entire world could not be created without the power of Shiv i.e. Shakti. Now Shiva and Its power Shakti create everything. This is the form of their togetherness that springs out of Lord Shiva. Shiva and Shakti though the same may also act independently. They are associated like the person and the action of the person. They are one and the same like the ice and the water - one becomes the other.

Shiva and his Shakti is a symbol of togetherness of to gender. Or can say two have to give support to eachother .whiout female this world is zero and men and women are placed equally by god.