What is a restrictive clause?

The term restrictive clause usually refers to a relative clause that follows a noun and limits the scope of the noun.

Example: The package that came last Tuesday is on your desk.

In the set of all possible packages, the restrictive clause picks out the one that the sentence is referring to-- the one that came last Tuesday. The restrictive clause answers the question "Which package are you talking about?"

Relative clauses that don't limit the scope of the noun are called non-restrictive. This kind of relative clause is set off by parenthetical commas.

Example: My mother, who loves to watch tennis, lives in University City.

There's only one eligible person in the set my mother. The information that she loves to watch tennis does not tell you which one of my mothers I'm talking about--it just adds to what you know about my mother.

Notice that in both my examples, there's a presumption that you and I are in a conversation and that I'm trying to make sure you and I are "on the same page." This is what makes defining this concept difficult--it's really about references established through discourse and it's hard to talk about out of context.

By the way, the example provided here earlier by a different contributor--

Her sister, who is a lawyer in New york City, is coming for the weekend.

--is marked by the commas as a non-restrictive clause. If the speaker has more than one sister and the clause is pinpointing which sister is being talked about, the same clause without the commas would be restrictive.