WARNING. MAY CONTAIN SPOILERS. Depending on how far you are in the anime.
The Rasengan is a techinque used by Naruto Uzumaki, Jarayia the toad sage (Also known as Pervy sage), and Minato Namikaze, the fourth Hokage of the Hidden Leaf Village.
The techinque was first created by the fourth hokage, but he wasn't able to fully devolop it before his death. When Jarayia taught Naruto the move, he was able to fully devolop it, and make many more techinque varitions from it, such as the Giant Rasengan, and the Wind-Rasenshuriken.
The Rasengan is a ball of pure swirling chakra, condensed down to the perferred size, and held in ones hand. Jarayia could form it with one hand, however in Naruto's case, he still has to make a shadow clone to form the Rasengan.
Unlike the Chidori
, (Lightening blade, or one thousand chirping birds) which uses massive amounts of chakra, and requires some level of Lightening style attack training, the Rasengan can be used several times in a battle, and would only require an above-average, if not basic level of chakra-control.
With devastating power, the Rasengan is also believed to be more powerful than the Chidori, it also doesn't require any hand signs, so it can be used at a moments notice. All this makes the Rasengan the ultimate weapon.