Use of he and she versus him and her

He and she are third-person, singular subject pronouns -- that is, they are used as the subject of a clause. He ran down the hill. She went to school.

His and her are third-person, singular possessive pronouns -- that is, they are used to indicate possession. His car would not start. Her books are in the bag.

Him and her are third-person, singular object pronouns -- that is, they are used to indicate the object of a verb's action. The dog bit him. He does not like her.

I hope this helps.