Possessive case is a grammatical case that exists in some languages and is used to indicate a relationship of possession. It is not the same as the genitive case, though the two have similar meanings in many languages.
See Possession (linguistics) for a survey of the different categories of possession distinguished in languages.
The English possessive
The term "possessive case" is often used to refer to the "'s" morpheme, which is suffixed onto many nouns in English to denote possession. This categorization is arguably not strictly correct — some grammarians contend that this affix is actually a clitic. By descent, however, the English usage does stem from a case ending, Old English -es. See genitive case for details.