Personality
Nagito first comes off as a polite, friendly, and easygoing, yet somewhat insecure boy. Hajime Hinata even mentions that his bright smile is very comforting. He was the only one that stayed with Hajime while he was unconscious, and expressed concern for his well-being, even after Hajime told him to go away. Though friendly with everyone, he is mostly interested in spending time with Hajime and can be quite clingy, and as a result, Hajime considers him a little annoying and not the most reliable, but still thinks he's a kind person.
Nagito attempts to be the team's conflict mediator and a poster boy for optimism, often encouraging others to be hopeful and to cooperate, however, he isn't taken very seriously. Hiyoko Saionji makes fun of him and considers his dramatic pep talks about hope and friendship embarrassing and tiresome. He is generally quite submissive and has a self-deprecating attitude, even agreeing with Hiyoko and the others' snide remarks.
Although he claims to be a pessimist, Nagito often appears unusually carefree; he lacks tact and occasionally says awkward, strange, and unsettling things without realizing it. At times he can also be more forceful; he is quick to scold Hajime when he's being too pessimistic or when he thought he was bullying Mikan Tsumiki. He is also notably annoyed by Teruteru Hanamura's treatment of girls and takes it upon himself to keep an eye on him to make sure he doesn't harass anyone.
Social Impairment
Overall, Nagito appears to be somewhat out of touch with his own feelings. He tries to be polite, but he can be overly harsh and insensitive, often without realizing it. He has a lack of social awareness and insight into his own behavior. Because of this, he has problems understanding how his own behavior can affect other people and he may not understand or pick up on social hints. He struggles with expressing himself in a socially appropriate manner and this often leads to people misunderstanding what he's trying to say, and vice versa. During Chapter 1's additional dialogue, Nagito explains that he says dubious things without meaning to and that he realizes this, but can't stop it from happening. However, he also adds that he always sincerely means what he says.
In Chapter 4 of Danganronpa 2, he accidentally offended both Kazuichi and Fuyuhiko Kuzuryu—in Fuyuhiko's case, he understood that he said something wrong and quickly apologized, but remained quite confused, and misunderstood what he said wrong. For Kazuichi, he was completely oblivious and only noticed that Kazuichi seemed angry for some reason. Other examples of this type of behavior include his odd and awkward sense of humor, often making jokes at inappropriate times, like soon after someone's death. He usually backs off if the others explain to him that his behavior is rude or he tells them he wasn't being serious. Similarly, when he tries to compliment someone, it can come across as an insult. His gauge of sarcasm is quite poor, too, as he sometimes mistakes mean comments for compliments. He also doesn't understand why the others are paranoid, angry and afraid of him. He's often confused by the others' behavior, thinking that they're strange for acting so suspicious of him, to the point that he sometimes worries about their mental health. He thinks that the others hate him because he's a lower human being.
In his final free-time event, Nagito claims to have Frontotemporal Dementia, a neurodegenerative disease that affects their personality and social cognition and thus may account for some of his strange behavior. He claims he was lying immediately afterward and it is unknown whether this was a lie or not. Nevertheless, it is clear that he has some type of psychological disorder.
It should be noted that Nagito's strange luck affects his condition as well, seemingly allowing him to live much longer than he should have, and likely giving him unusual symptoms.
Ultimate Lucky Student
Nagito got his title as the Ultimate Lucky Student by winning a lottery out of completely ordinary students, which led to him joining Hope's Peak Academy. He at first declined, saying that he didn't deserve it, but they insisted that he should attend. Nagito possesses a cycle of consistent good and bad luck. Whenever something extremely lucky happens to him, something extremely unlucky is bound to happen soon after. While the talent seems to protect him from death, it can cause him great suffering and has killed many people around him. The only person whose luck matches his own is Izuru Kamukura, and later Hajime.
Nagito's birthday (the 28th day of the fourth month) heavily references his talent, with his birth month representing bad luck and death while his birthday represents a double amount of wealth and fortune according to old Japanese and Chinese beliefs. Considering some of the supernatural elements seen in the series, it's possible that his unusual birthday might have an impact on his unusual luck.