Avatar is a concept within Hinduism that in Sanskrit literally means 'descent'. It signifies the material appearance or incarnation of a powerful deity, or spirit on Earth. The relative verb to "alight, to make one's appearance" is sometimes used to refer to any guru or revered human being.
Hindu god Vishnu (centre) surrounded by his ten major avatars, namely Matsya; Kurma; Varaha; Narasimha; Vamana; Parashurama; Rama; Krishna; Buddha, and Kalki
Mohini, the female avatar of Vishnu (statue at Belur temple, Karnataka.)
Sharabha (right) with Narasimha (18th-century painting, Pahari/Kangra School)
Jhulelal, incarnation of Varuna
Incarnation literally means embodied in flesh or taking on flesh. It is the conception and the embodiment of a deity or spirit in some earthly form or an anthropomorphic form of a god. It is used to mean a god, deity, or Divine Being in human or animal form on Earth. The proper noun, Incarnation, refers to the union of divinity with humanity in Jesus Christ.
Christ Pantocrator, God incarnate in the Christian faith, shown in a mosaic from Daphni, Greece, ca. 1080–1100.
Ten incarnations of Vishnu (Matsya, Kurma, Varaha, Vamana, Krishna, Kalki, Buddha, Parshurama, Rama & Narasimha). Painting from Jaipur, now at the Victoria and Albert Museum