In the world of grammar and writing the 'person' refers to the person you are speaking about. In writing, 'person' specifically refers to the person who is speaking in a written work -- in other words, the person that the writer is 'speaking' about.
The first person is nearly always I: the sentence "I want that" is written in the first person. Technically, this is the first person singular; one can also use the first person plural, we. "We will rock you" is written in the first person plural.
The second person is you. The sentence "You are a beautiful and unique snowflake" is written in the second person. 'You' is technically its own plural, but you can, if you wish, write or speak in the second person plural by using y'all or yous.
The third person is he, she, it, and they. Examples include "They walked to the store"; "He stole the cookies"; "It was a monster from outer space".
The fourth person is rarely referred to or used. Most often it refers to an indeterminate person, for example "One does not simply walk into Mordor". There are a number of 'indefinite referents' that would qualify as fourth person speakers: somebody, someone, something, anybody, anything, everybody, everything, nobody, and nothing are all examples. You will very rarely find a story written in the fourth person.
The term is also used in a more technical sense in linguistics, where it is used to refer to the obviative third person. When there are two 'third persons' in a sentence, one is the proximate (the subject), and one is the obviative (the object). In the sentence "He likes her nodes", He is the proximate, and she (or 'her') is the obviative. In some languages (not English), the obviative uses a separate grammatical marker (the technical term for this is obviative person deixis). To the best of my knowledge the only languages with this sort of grammatical marker are Native American languages, including Ojibwe, Algonquian, Arapaho, and Comanche.
I would like to link some well written fictional pieces that are written in the fourth person. If you have any examples, please msg me.
So far we have: