The antecedent of a pronoun is the word the pronoun refers to. There are several style problems which writers and speakers sometimes have when they do not match the pronoun and the noun it replaces correctly.
Missing or Mismatched Antecedent
A pronoun, unless it is an indefinite pronoun, must have an antecedent, a word it refers to. The pronoun must match the word it replaces--singular or plural, and, sometimes, masculine or feminine.
Incorrect: Every student must have their pencils.
(Both every and student are singular; therefore, his, her, or his or her must be used. Their is plural and cannot refer to a singular noun.)
A pronoun's antecedent must be clear.
Incorrect: I never go to that place because they have stale bread.
(What does they refer to? Both I and place are singular.)
Correct: I never go to that place because it has stale bread.
When the antecedent is a different gender, person, or number than the pronoun it is supposed to replace; this is sometimes called a "faulty co-reference."
Incorrect: Politics is my favorite subject. They are such fascinating people.
Correct: Politics is my favorite subject. Politicians are such fascinating people.
Faulty co-reference may also occur with adverbs that do not replace an adverbial expression or pronouns that do not replace nouns.
Incorrect: He ought to speak French well. He lived there for twenty years.
Correct: He ought to speak French well. He lived in France for twenty years.
A pronoun's antecedent must be unambiguous. Sometimes there may be more than one word the pronoun could refer to. In a case like that, it may be better not to use the pronoun.
Incorrect: The suitcase was on the plane, but now it's gone.
(What is gone? The suitcase or the plane?)
Correct: The suitcase was on the plane, but now the suitcase is gone.
ORThe suitcase was on the plane, but now the plane is gone.
(Depends on which you mean...)
The pronoun must be close enough to the word it is replacing so that your reader knows whom or what you are talking about.
Unclear: Buford saw Longstreet's division coming toward his men. Reynolds' troops responded quickly to the calls for assistance, and soon he found himself in the midst of a deadly battle.
(Who is he? Buford, Reynolds, or Longstreet?)
Clear: Buford saw Longstreet's division coming toward his men. Reynolds' troops responded quickly to the calls for assistance, and soon Buford found himself in the midst of a deadly battle.
See also Using Indefinite Pronouns.