The Avatars are bending arts masters who are chosen by the Gods and are the only bender who can master all four elements. A bender was native from either The Air Temple, Fire Nation, Water Tribe or Earth Kingdom. Which ever nation they’re indigenous to already know that element and must travel to the other 3 nations to learn the other elements. The current Avatar Aang who was The Last Airbender was destined to restore balance to the world by defeating The Fire Lord.
They many afters like Avatar roku and later sometime after the events of Avatar the last Airbender Korra the titular character from the Legend of Korra series is now the current avatar.
The Avatar is the only being which can master the four elements and can energybend as well. It first came to existence 10,000 years before the main story, as the result of a permanent fusion between Wan - the first man to not only possess the power of more than one element, but the first human bender as well - and Raava, the spirit of light and peace. The Avatar is a reincarnation of Wan throughout the millennia, starting a cycle that began the moment Wan died.
The Avatar is able to access the power of Raava and his or her previous incarnations in what is called the Avatar State, giving them unlimited power for as long as they are in said state. However, any given incarnation of the Avatar is not immortal, and if he or she is killed in the Avatar State, the Avatar Spirit will die and the cycle will end (though Raava herself will survive the death of the Avatar Spirit, and will eventually reform elsewhere).
The Avatar's mission in life, a task set forth by Wan himself, is to maintain balance of the world, as well as between the mortal and spirit realms. This job includes bringing peace between groups in conflict, or defeating threats to world peace such as imperialist tyrants bent on conquest. The Avatar is also the spiritual leader of the world; due to being half spirit, the Avatar is most powerful in the Spirit World, as opposed to other humans who normally are powerless in comparison. The Avatar must master the four elements and attain a certain degree of balance within themselves; they are then referred to as a "fully realized Avatar".