The case of a noun or pronoun determines how you can use it in a phrase or clause. There are three cases in Modern English (as opposed to eight in Classical Latin, four in German, and only two in French):

Subject

You use the subject case for a noun or pronoun which stands alone, is the subject of a clause, is the subject complement, or stands in apposition to any of these.

Object

You use the object case for the object of a preposition, a verb, or a verbal, or for any noun or pronoun which stands in apposition to one of these.

Possessive

You use the possessive case for any noun or pronoun which acts an an adjective, implicitly or explicitly modifying another element in the sentence. 

Nouns always take the same form in the subject case and the object case, while pronouns often change their form. Both nouns and pronouns usually change their form for the possessive case:

Subject Case

The man travelled to Newfoundland.

He travelled to Newfoundland.

Object Case

The taxi drove the man to the airport.

The taxi drove him to the airport.

Possessive Case

The baggage handlers lost the man's suitcase.

The baggage handlers lost his suitcase.

For further information, see possessive nouns, possessive pronouns, and possessive adjectives.