Nouns and pronouns are either singular or plural. Nouns typically form their plurals by adding ‑s, (boys), ‑es (torches), or ‑ies (cities). Some plural words, like children and fish, do not use ‑s. Pronouns have special forms to show plurality (I and we, he and they, it and they, she and they) (examples in subjective case).
If the grammatical subject of a sentence is singular, then the verb must be singular. Also, if an antecedent is singular, then any pronoun referring to it must be singular.
These days—to avoid the he/she problem—writers will use a singular antecedent and then refer to it with the plural pronouns they, their, or them. Though this usage is correct in England, it would not be acceptable in formal writing in America even though everyone does it in oral speech. The following is incorrect in formal writing:
An applicant must file their application with the personnel office. You can avoid the problem by making the antecedent plural (applicants).