Possessive is an adjective meaning “jealous” or “having the desire to own or dominate.” In a grammatical sense, it’s used as a noun or adjective referring to the ways in which possession (ownership) is shown in language.
Some grammatical concepts involving the word are possessive pronouns (e.g., “my”), possessive nouns (e.g., “Steven’s”), possessive apostrophes (apostrophes like the one in “Steven’s”), and possessive case (how words show possession in general).