"Person" refers to the subject of the verb. If the subject is the speaker, the verb is in the first person--in other words, the 1^st person subject pronoun is "I". The 2nd person is "you", and the 3rd person is "he'" "she," or "it."

In Latin, the "person" of a verb is indicated by its ending letters. 1st person verbs end in -o; 2nd person verbs end in -s; and 3rd person verbs end in -t.