It's about this boy, Light, who found this notebook, and with it came a Shinigami. (A phantom type thing) And it stated that who ever's name is placed in the book shall die. And if you don't specifiy the cause of death, the person shall just die of a heart attack. So, without anyone knowing, Light tests the notebook by killing criminals. Although, people have become suspicious, and have tried to catch him. They call this person killing the peope, Kira. And then it goes on to tell about Kira leaving notes and controling the actions of people before they die. But now, at the end of the third book, the people of the city have figured out that there is another Kira; a second one!
This is just a sketchy overview of the book, it goes a bit more into details about him being suspected as Kira and him being watched and everything but...