Akatsuki, which means Daybreak when translated in English, was founded by three orphans named Yahiko, Konan, and Nagato.
The Origins of Akatsuki
The organization at the time consisted of Amegakure ninja that wanted to create peace for their homeland, which at the time was a major battleground for three of the five great countries during the Third Shinobi World War. They had a larger goal of attaining world peace, which Yahiko believed could be done by Nagato as he possessed a legendary ability called the Rinnegan. Though it has been stated by Konan that everyone acknowledged Yahiko as the true leader. The leader of Amegakure, Hanzo, felt threatened by this groups presence and under the guise of wanting to meet to aid in Akatsuki's goals ambushed them. Hanzo captured Konan and forced Nagato to kill Yahiko in order to save her life. After Yahiko forces Nagato to do it, Nagato becomes enraged and summons the Demonic Statue of the Outer Path to obliterate Hanzo's forces. Nagato took over as leader of Akatsuki and waged a civil war that conquered Amegakure and killed Hanzo. Though he lost his ability to walk Nagato began using six other bodies, one of which was Yahikos, a vessals allowing him to run the organization. He also took the name Pain, because he believed that only after the world experienced great pain would it desire true peace. Pain would also form an alliance with Obito Uchiha, who unbeknownst to Nagato gave him his Rinnegan powers and aided in the gathering of new members.
Akatsuki under Pain
Pain developed a new plan to attain world peace using Akatsuki that involved three stages. First they obtain a large amount of money to support their organization. The second part is to then act as a mercenary group that can offer services below the cost of other ninja villages, because of the money they have obtained. This would cause the shinobi village's economies to suffer. They would also during this time capture the Tailed Beasts, creatures with immense chakra sealed away inside hosts, and use them to attack shinobi villages. All of this would cause the shinobi villages to collapse making Akatsuki the sole military power. The third stage involves the Akatsuki using it's military power to conquer the world. Pain would then grant the Akatsuki members any wish within his power as thanks for their services. Unlike the original Akatsuki, most of the new members joined to further their own goals rather then a belief in world peace.