The most important thing to remember about the grammatical person is that people are not "persons." Rather the grammatical person indicates a relationship between two specific people (or things):
Three different relationships are distinguished:
You can distinguish among first, second and third persons by noting their
distance from the speaker (or writer). If the speaker is the doer of the action
of the verb, then that is the closest relationship possible between the speaker
of the sentence and the subject of the sentence. There is but one person
involved. If the one spoken to (the hearer or the reader) is the doer
of the action of the sentence, then there are two players involved
the speaker (writer) of the sentence and the doer of the action (the hearer
or the reader), thus a second person is involved. If the doer of the
action of the sentence is neither the speaker (or writer) nor the hearer (or
reader), then a third person is involved in the relationship between speaker
(or writer) and the subject of the sentence.
If the subject is expressed
in a sentence (as a noun or noun-like thing), the verb will be third-person.