Person refers to the point of view you use in your writing. Simple as that.
When you use the pronouns I or we, that's first person. Since first person expresses the writer's perspective, it's used most often for personal or autobiographical writing like memoirs.
That's why you've probably had a teacher or two (or ten) tell you not to use I in your academic writing: it can make your writing seem less objective. So save first person for your personal essays and that triple-locked diary you keep hidden in the bottom of your underwear drawer.
When you address the audience using the pronoun you, that's second person. You'll spot second person most often in advertising, correspondence, and business or technical writing. Makes sense, right? Advertising tries to zero in on the consumer and convince you—yes, you!—that you simply can't live without the new Chop-O-Matic Pocket Smoothie Maker. Letters and emails are addressed to a specific person. And business and technical writing are often process-oriented and instructional in nature.
Last (but certainly not least) there's ye olde third person, which uses the pronouns he, she, it, or they. Writing in third person creates an objective, impersonal narrator, which makes it perfect for most formal academic writing.
The point of view you use depends on your purpose and audience, but no matter which perspective you choose, you must remember this: be consistent. When a paper switches between points of view, it messes with the reader's head. So if you start with third person, you better finish with third person… unless you want a bunch of confused readers wandering around your front yard.
Here's a quick and easy way to check your perspective: First, identify the subject of the sentence. If that subject is talking about itself, that's first person. If the subject is being spoken to, that's second person. If the subject is being spoken about, that's third person. Easy-peasy.