Death Note begins with Ryuk and the other death gods in the Shinigami Realm. Ryuk was bored with the lack of activity, as all the death gods are relaxing. So, he decides to obtain a second Death Note by tricking the Shinigami King, before writing the instructions in English and dropping it into the human world. The plot of the series truly begins when Light Yagami finds the Death Note on his school grounds.
Five days later, Ryuk has a conversation with Light. The simple reason he gives about why he dropped the Death Note into the human world is that because he is bored. He then tells Light that, since he was the one who found the notebook, it belongs to him. If he does not need it anymore, he can pass it to anyone else. But when it is the time for Light to die, Ryuk will write his name down. Light then explains to Ryuk that he wishes to cleanse the world of evil criminals, and becomes the God of the new world. Ryuk tells Light that, if he were to do that, the only bad person left would be Light himself. Light ignores his comment, maintaining that he is entirely sincere. Ryuk then comments that humans are interesting.