Pronouns have different forms based on their function within a sentence. Pronoun case refers to the different forms a pronoun can take.
There are three pronoun cases: nominative, objective, and possessive. The nominative case is used for the person speaking. The objective case is used for the person spoken about. The possessive case is used for the person spoken to.

Nominative Objective Possessive
he him his
I me mine, my
it it its
she her hers
they them their, theirs
we us our, ours
who whom whose
whoever whomever whosever
you you your, yours

Use the nominative case when the pronoun is the subject of a sentence or a clause:

I wrote the letter.

-- "I" is the subject pronoun.

Use the possessive case to modify a preceding or following noun:

My car is in the shop.

-- "My" is the pronoun

That car of mine is in the shop.

-- "Mine" is the pronoun

Use the objective case when the pronoun is a direct object, indirect object, or the object of a preposition:

Yesterday she told me.

-- "Me" is the object.

She told me about what happened.

-- "Me" is the object.

It was told to me by her.

-- "Me" is the object of the preposition "to."