Avatar is a concept that is unique amount all Dharmas and religions. The word itself, derives from the Sanskrit word, 'avatarana,' which means 'descent'. In English, its synonyms are incarnation and manifestation, while "emanation" and "embodiment" can also be used equivalently.
So, literally, Avatar means God descended to earth in a form (human or another form). As per the Bhagavad Gita, God descends to earth in every Yuga whenever Adharma becomes prominent to annihilate the miscreants and to re-establish the principles of Dharma.
In English, it can be called incarnation/reincarnation, emanation, and manifestation.
- Bhagavad Gita, Chapter 4, Verse 7,8