Ardhanari Krishna is the half man – half woman form of Sri Krishna and is quite similar to the unique and most important concept of Ardhanarishvara (combined form of Shiva and Goddess Parvati).
In Ardhanari Krishna, half part of Krishna is Radha and it is mentioned in the Brahma Vaivarta Purana. As per the purana, right half of Bhagavan Sri Krishna is himself and the left half is Radha.
A unique murti (vigraham or sculpture) of this concept was found at Chaul, Maharashtra, and is known as Ardha Radha Venudhar Murti. This rarest of rare sculpture has ten arms. The left half of the murti is of brass depicting Bhagavan Sri Krishna whereas right half is made of copper depicting Radha Rani. In this form, the deity plays flute with two frontal normal hands of both the male and female.
The concept of Ardhanari Krishna is a continuation of the ancient concept of Ardhanarishwara. Upanishads very clearly teaches us that there is no second here. There is only That (Tatvamasi). Krishna and Radha are two different bodies to the ignorant devotee. To the one who has overcome maya or illusion they are one – Radhakrishna.