Otonashi lost his memory in an accident and thus thinks his life has no meaning. Things start to change for him as the story progresses. He is the main male protagonist of Angel Beats!
In episode 7, Naoi is asked by Yuri to hypnotize him so he can regain his memories. This turns out successful revealing he had a very ill younger sister who was his sole reason for living. After her death, Otonashi decides to become a doctor to cure others who are ill like his sister and starts to study frantically. On his way to take an exam, his train crashes because of a snow storm. This hints that he died at that moment.
However in episode 9, it is shown he survives the crash and starts helping the other few survivors as much as he can, since he was studying medicine. He and the survivors are stuck in a dark tunnel and it is only after 7 days that a rescue team arrives. A few minutes before losing all hope, Otonashi signs a paper to donate his organs (and inspires the other survivors to do the same). Otonashi dies soon after, just seconds before the rescue team arrived.
Over the course of the anime, he is the first of the SSS to try and understand Tenshi (Kanade).
In "another epilogue," which is an alternate ending to the original ending of the anime, Otonashi is seen to have remained as the new student president. He faces another soul and inspires him to face up to their past. Though the episode is ambiguous, it is clear Otonashi had decided to remain behind in Purgatory whereas everyone has already left, as he stated in his final Dialogue with Kanade.