From the internet
Ardhanarishvara (Sanskrit: अर्धनारीश्वर, the half-female Lord), is a form of the Hindu deity Shiva combined with his consort Parvati. Ardhanarishvara is depicted as half-male and half-female, equally split down the middle. The right half is usually the male Shiva, illustrating his traditional attributes.
The Ardhanareeshvara represents a constructive and generative power. Ardhanareeshvara symbolizes male and female principles cannot be separated. It conveys the unity of opposites in the universe. The male half stands for Purusha and female half is Prakriti. Ardhanareeshvara harmonizes the two conflicting ways of life: The spiritual way of the ascetic as represented by Shiva, and the materialistic way of the householder symbolized by Parvati. It conveys that Shiva and Shakti are one and the same. A human being is not a pure unisexual organism. Each human organism bears the potentiality of both male and female sex. Neurohormonal mechanisms have been found to be greatly influencing the sexual behavior. The modern world has come to understand the concept of “Ardhanareeshwara” as it aspires to resolve the paradox of opposites into a unity, not by negation, but through positive experiences of life. The matching of opposites produces the true rhythm of life.
The earliest Ardhanarishvara images are dated to the Kushan period, starting from the first century CE. Its iconography evolved and was perfected in the Gupta era. The Puranas and various iconographic treatises write about the mythology and iconography of Ardhanarishvara. Ardhanarishvara remains a popular iconographic form found in most Shiva temples throughout India, though very few temples are dedicated to this deity.
Ardhanarishvara represents the synthesis of masculine and feminine energies of the universe (Purusha and Prakriti) and illustrates how Shakti, the female principle of God, is inseparable from (or the same as, according to some interpretations) Shiva, the male principle of God, and vice versa. The union of these principles is exalted as the root and womb of all creation. Another view is that Ardhanarishvara is a symbol of Shiva’s all-pervasive nature.
The Shiva Purana describes that the creator god Brahma created all male beings, the Prajapatis, and told them to regenerate, which they were unable to do. Confronted with the resulting decline in the pace of creation, Brahma was perplexed and contemplated on Shiva for help. To enlighten Brahma of his folly, Shiva appeared before him as Ardhanarishvara. Brahma prayed to the female half of Shiva to give him a female to continue creation. The goddess agreed and created various female powers from her body, thereby allowing creation to progress.
You should also read this dimension of the concept of Ardhanariswar-