* When Big Dog snuck under the fence, Big Dog ran to the dumpster.
* When Big Dog snuck under the fence, he ran to the dumpster.
Clearly the second sentence sounds better.
A pronoun renames (takes the place of) a noun that comes before it.
An antecedent is what we call the noun that comes before the pronoun.
Two examples should be enough:
1. I get worried when the neighbors let their dog out.
2. The dog goes wild, and he always messes up my front yard.
In number 1, neighbors is the antecedent; their is the pronoun. They agree because both are plural. In number 2, dog is the antecedent, and he is the pronoun. They agree since both are singular. If you are having problems with pronoun-antecedent agreement, underline all your pronouns; then, locate the antecedent for each. Make sure that both are the same in number. That's all you have to do.
A common stylistic problem in writing, often leading to ambiguity, is the use of a pronoun for which the antecedent is not clear, as in the following example:
* I met John at Mike's party. He told me about his new friend.
Did John tell the speaker about his own new friend? Did John tell the speaker about Mike's new friend? Did Mike tell the speaker about his own new friend? Or did Mike tell the speaker about John's new friend? Generally most competent speakers would agree that "he" refers to "John."
Another issue is the use of a pronoun and anaphor which differ in number, for example "Everyone had their own sleeping bag." The words everyone and everybody are singular, meaning every "one" and every "body". Thus neither of those words should be used with the plural anaphor "their." "Each student" is singular, but requires the use of the gender-inclusive "his or her" which is often seen as awkward. The sentence "Each camper had his or her own sleeping bag" is thus correct but inelegant. This is a question of writing style rather than grammar when analyzed to this point. The sentence "All the campers had their sleeping bags" is clearer.
You can find my sources here and here and here
Taken from the book Painless Grammar (Painless Series)
by Rebecca Elliott
by Rebecca Elliott