Certain pronouns called possessive pronouns show ownership. Some are used alone; some describe a noun.
Used alone: mine, yours, his, hers, ours, theirs, whose
Correct: That computer is hers.
Modify noun: my, your, his, her, its, our, their, whose
Correct: That is her computer.
Please note that none of the possessive pronouns are spelled with an apostrophe. See Apostrophes with Pronouns for more on this.
Possessive Pronouns with Gerunds
Possessive pronouns are used to describe gerunds. Using the objective case confuses the reader.
Incorrect: You winning in spite of the odds inspired us all.
(Ambiguous and awkward. Do you inspire or does the winning inspire?)
Correct: Your winning in spite of the odds inspired us all.
Incorrect: We could not stand him whining about everything.
(Which could you not stand? Him? or His whining?)
Because of the possible confusion, use possessive pronouns with gerunds.
Correct: We could not stand his whining about everything.