What are the first-person, second-person, and third-person points of view? Which is used for formal essays?

The first-person point of view is used mainly in fiction, when a story is told from the point of view of one of the characters, using "I" and "me" throughout the story. This point of view allows the reader to see all the action of the story through the eyes of that single character; when the "I" of the story is the main character, the reader can, quite literally, get "in the head" of the narrator, experiencing all of the main character's thoughts and feelings. You would rarely use this point of view in a formal essay, because when writing an essay, you usually want to remain objective in the argument you're presenting.

The second-person point of view isn't used very much, simply because it's very difficult to write from this point of view without confusing the readers (who might think the author is addressing them). This point of view is also used mainly in fiction, when the story's narrator uses "you" to address the main character, such as in a story where the author (narrator) is addressing a younger version of himself. Such a point of view would also be inappropriate for a formal essay.

The third-person point of view is the one you want to use for a formal essay. In this point of view, the author uses "he" and "she" to describe the action of the story. This point of view allows for distance between the author and the characters, as well as for an "all-seeing, all-knowing" (or omniscient) narrator. Using this point of view in a formal essay enables you to be objective in the argument you're presenting and not bring your personal feelings, thoughts, or experiences into the essay.