An Avatar is an incarnation of God. When God comes down to earth in any life-form, then we call him an Avatar.
In the Bhagavad Gita it is written,
"Whenever there is decay of Dharma (Righteousness) and outbreak of Adharma (non-Righteousness), I descend myself to protect the good, to annihilate the wicked and to re-establish Dharma (Righteousness). I am born from age to age."