In semantics, a modifier is said to be restrictive (or defining) if it restricts the reference of its head. For example, in "the red car is fancier than the blue one", red and blue are restrictive, because they restrict which cars car and one are referring to. ("The car is fancier than the one" would make little sense.) By contrast, in "John's beautiful mother", beautiful is non-restrictive; "John's mother" identifies her sufficiently, whereas "beautiful" only serves to add more information.
Restrictive modifiers are also called defining, identifying, essential, or necessary; non-restrictive ones are also called non-defining, non-identifying, descriptive, or unnecessary (though this last term can be misleading). In certain cases, generally when restrictiveness is marked syntactically through the lack of commas, restrictive modifiers are called integrated and non-restrictive ones are called non-integrated or supplementary.
Restrictiveness in English
English does not generally mark modifiers for restrictiveness. The only modifiers that are consistently marked for restrictiveness are relative clauses: non-restrictive ones are set off in writing by using commas, and in speech through intonation (with a pause beforehand and an uninterrupted melody), whereas restrictive ones are not. Furthermore, although restrictive clauses are often headed by the relative pronoun that or by a zero relative pronoun, non-restrictive clauses are not. For example:
(*In formal American English, the use of which as a restrictive pronoun is often considered to be incorrect. See That or which.)
Although English does not consistently mark ordinary adjectives for restrictiveness, they can be marked by moving them into relative clauses. For example, "the red car is fancier than the blue one" can be rewritten as "the car that's red is fancier than the one that's blue." "John's beautiful wife" can be rewritten as "John's wife, who is beautiful", to avoid the suggestion of disambiguation between John's various wives. English speakers do not generally find such locutions necessary, however.