The concept of Ardhanäriswara is unique in Hindu religion. It represents the Lord as the abhinna-nimitta-upädäna-kärana of this manifest jagat. The left side represented by Sakti/Pärvati/Devi is the Prakrti, the upädäna-kärana – the material cause of the jagat. The right side represented by Siva is the nimitta-kärana – intelligent cause of the jagat.
In Advaita Vedänta, mäyä is not an independent or parallel entity. She is ‘brahmäsrayä mäyä’. Hence, the female form is shown integrated into the male form.
There are Puränic stories/explanation of this form. However, my understanding is as above.