Harihara is the name of a combined deity form of both Vishnu (Hari) and Shiva (Hara) from the Hindu tradition. Also known as Shankaranarayana ("Shankara" is Shiva, and "Narayana" is Vishnu), Harihara is thus worshipped by both Vaishnavites and Shaivities as a form of the Supreme God, as well as being a figure of worship for other Hindu traditions in general. Harihara is also sometimes used as a philosophical term to denote the unity of Vishnu and Shiva as different aspects of the same Supreme God. The exact nature of both Vishnu and Shiva (from their associated stories in Vedic and Puranic scriptures), and their position of difference or unity (or both), is a subject of some debate amongst the different philosophical schools.
Due to the fluid and diverse nature of Hinduism there are a wide variety of beliefs and traditions associated with both Vishnu and Shiva. Some schools hold that only Vishnu (including his associated Avatars) is the Supreme God, and others that Shiva (including his different incarnations) is actually the Supreme being. Some argue that both Shiva and Vishnu are the Supreme God-both being different aspects of the one person; and there are others still who regard the Supreme God as being ultimately formless (advaita, no material form) and thus see both Vishnu and Shiva as different facets of the one formless Brahman, with no material form.
Depending on which scriptures (and translations) are quoted, evidence is available to support each of the different arguments. In most cases, even if one personality is taken as being superior over the other, much respect is still offered to both Vishnu and Shiva by the other's worshippers (i.e. Shiva is still regarded as being above the level of an ordinary jiva and 'the greatest of the Vaishnavas' by Vaishnavas who worship only Vishnu).
Depiction In Art:
Harihara is depicted in art as split down the middle, one half representing Shiva, the other half representing Vishnu. The Shiva half will have the matted locks of a yogic master piled high on his head and sometimes will wear a tiger skin, reserved for the most revered ascetics. Shiva's pale skin may be read as ash-covered in his role as an ascetic. The Vishnu half will wear a tall crown and other jewelry, representing his responsibility for maintaining World order. Vishnu's black skin represents holiness. Broadly, these distinctions serve to represent the duality of humble religious influence in the ascetic and authoritative secular power in the king or householder. However, in other aspects Shiva also takes on the authoritative position of householder, a position which is directly at odds with the ascetic position depicted in his Harihara manifestation.