genitive NP: English the donkey of Sam, Sam's donkey
adjective phrase: English the old tree
relative clause (restrictive): English the house that is green
The term with this meaning is particulary common in the grammatical traditions of German (Attribut, Beifügung) and Russian (opredelenie). The term attribute in this sense is not so common in English, though the adjective attributive is widely used.
See also predicative attribute.
From Latin attributum 'what has been attributed'. First attested in this grammatical sense in the early 19th century.