A restrictive clause is a kind of relative clause that resolves ambiguity in a sentence by modifying the noun immediately preceding it.1 In English (and many other languages), a restrictive clause is rarely preceded by a comma.

Consider this example:

I would like to eat a piece of cake that contains no chocolate.

The restrictive clause, "that contains no chocolate," clarifies the ambiguity of "piece of cake;" that is, it clarifies that the speaker does not just want to eat ANY piece of cake, but rather it restricts the kinds of cake to only those containing no chocolate.

Here's a useful rule of thumb to help you distinguish a restrictive clause from its fraternal twin, non-restrictive clause, (also called a descriptive clause):

If the clause contains a comma before the "that" or "which" (or "who", or "when"), it is NOT restrictive.

In our example, using a comma would not make sense, reading, "I would like to eat a piece of cake, that contains no chocolate.") Think of "cake-that-contains-no-chocolate" as single concept, a single "word" of sorts.

Distinguishing restrictive clauses from descriptive clauses may be useful because of its application in determining how to use the words "which," or "that," in ways which satisfy prescriptive grammarians.

SEE: That vs. which for more.

1. Interestingly, this very sentence--well, not THIS one, but the sentence where the "1" is-- here contains an example of a restrictive clause; the phrase, "a phrase that resolves ambiguity" is itself a restrictive clause! If this is confusing, just ignore it, though; the 'official' example I've provided should be more clear.