Speaking in the first person comes naturally because we do it all the time. Further, we are used to listening to people tell stories in the first person, so this perspective works well as it is the same way we process oral accounts. The narrator and the main character are also the same person, so this fills in the gap that arises when writing in the third person and having an "outside" voice coming into the narrative.
The first person account gives the narrative credibility, because the protagonist is telling the story. No matter if the narrative is an autobiography or a science-fiction thriller, the reader wants to see the action as it happens and the first person is the expert who is at the scene relating things as they unfold. By the same token, the first person can recall past events that relate to the incident or speculate on what may happen next.
Another advantage of writing in the first person is that you share your secrets and insights with the reader. Because the reader is privy to the first person's inner most thoughts, a relationship -- a friendship of sorts -- develops between the reader and the narrator.
Character development is another advantage of writing in the first person. Rather than having a cast of two or three main characters, the first person account lends itself to the entire narrative being filtered through one person's point of view. Supporting characters are then developed in relation to the central person.
The first person narrator assumes can assume a reflective voice while relating events that have happened. Like confiding in the reader, the first person describes what was learned from the experience and how it affected or changed his life. It reinforces the advantage that writing a narrative in first person has of being able to speak directly to the reader, rather than having to go through scenes where the protagonist's character is developed through other characters or situations.