Naruto is a shounen series created by Kishimoto Masashi. It was first serialized in 1999 in Weekly Jump, and began airing on TV Tokyo in 2002.
The series centers around the lives of Konoha's finest ninjas, including Uzumaki Naruto - the aspiring Hokage and fun-loving prankster of the Konoha village. Twelve years ago, a terrible fox demon wrecked havoc on the village, and the brave Yondaime sacrificed his own life to seal the Kyuubi within a newborn baby. As fate would have it, that baby was Naruto, and throughout the series, we see the hardships and happiness he faces everyday, fighting for justice and going for his dream.
Akatsuki is a criminal organization comprised of nine S-class criminals from across the shinobi villages. The members travel in pairs, collecting jutsus and information for the organization. (The word akatsuki means dawn, or literally, "red moon.")
Their first appearance is made halfway into the first arc, where we are introduced to Uchiha Itachi and Hoshigaki Kisame. However, they flee when faced against the great Jiraiya, and leave behind many unanswered questions: What is Akatsuki's intentions? Who is their leader? Why are they after Naruto's kyuubi?
What's with the purple nail polish?
These questions are slowly starting to get answered in the second arc of Naruto (after the timeskip), as Akatsuki is involved in a significant part of the storyline. New members are introduced, and their motives are revealed.
Naruto and his comrades first start pursuing Akatsuki because they believe it will lead them one step closer to Sasuke. Since Orochimaru used to be a part of the organization, they believe that defeating Akatsuki will lead them to Orochimaru and eventually, to save Sasuke.