This question has two parts, because it can refer to Baldwin's fiction, especially Go Tell It on the Mountain, and his non-fiction essays in Notes of a Native Son, Nobody Knows my Name, and The Fire Next Time. In these latter works the author writes with an imaginative sweep that makes his literary voice emblematic of a "character" as in a novelistic narrative.
In Go Tell it on the Mountain, the story, from the opening pages, is told from John's point of view, since John is clearly the author's persona. Every author who writes a more-or-less autobiographical novel is essentially turning himself/herself into a "character" simply by writing the novel. What, however, makes such a character convincing or credible? It's chiefly through an accumulation of detail, by showing the daily events in the character's life. It is not merely through individual moments, such as John's mother giving him a gift, where we begin to understand his character more fully, but through the turmoil we see in John's family that affects him so profoundly. We also see more of John's character through the flashback technique Baldwin uses, showing the histories of John's mother, his stepfather, and his biological father (the details of the latter's story, Baldwin stated, were largely invented). It is a family saga in which the interplay of history and personal stories have a cumulative effect of enhancing our understanding of John himself, John's family, the church, and the story of America overall.
In his essays, Baldwin takes an approach in which that same personal story has a symbiotic relation to the events surrounding him on which he is commenting. In "The Harlem Ghetto," for instance, he analyzes the complex relationship between the African-American and Jewish communities. His general observations are interspersed with his own recollections of his father's traumatized and, hence, violent attitude about the outside world. In sharing these experiences, Baldwin projects himself as a character that not only reflects the national dynamic, but the constants of world history as well. It is something that has extended beyond the mere fact of an essayist's personality shining through in his writings, as with George Orwell, for instance (though Orwell also becomes a character in some of his essays). Baldwin's disagreements with other writers, such as Richard Wright and Norman Mailer, are central to his canon of essays. Similarly, his description of his meeting with Nation of Islam leaders is both highly personal and even novelistic in its way—though objective and reasoned—and is still relevant now, nearly sixty years later.