The narrator's voice is third-person (but omniscient, which means he/she is all-knowing). An omniscient narrator can see into the minds of the character or characters.
In this novel, Joyce's subject is Stephen Dedalus, the main character. There is little chronology to the novel, as Joyce presents view of Dedalus at different time periods of his life:
There is no plot as such in the novel; the narrative is not continuous but fragmented, with gaps in the chronology. The focus is exclusively on the central character, Stephen Dedalus, who is present on virtually every page. Every narrative detail is filtered through Stephen’s consciousness. (eNotes)
In early portions of the novel, Stephen is young, so the language that Joyce uses is different. It is simpler and less complicated, but as Stephen grows up, the language becomes more "mature." Joyce uses this type of narration to show the reader how Stephen matures throughout his life.