Restrictive and Nonrestrictive Adjectives Clauses

What are adjective clauses?
First of all, it’s important to understand the meaning of a clause. A clause is a group of related words that contain a subject and verb. So, an adjective clause is a group of related words with a subject and verb that describes a noun or pronoun. An adjective clause is also always dependent which means it cannot stand alone as a sentence.
Nonrestrictive Adjective Clauses
A nonrestrictive modifying clause (or nonessential clause) is an adjective clause that adds extra or nonessential information to a sentence. The meaning of the sentence would not change if the clause were to be omitted. Nonrestrictive modifying clauses are usually set off by commas.
Here's an example:
Old Professor Legree, who dresses like a teenager, is going through his second childhood.

This who clause is nonrestrictive because the information in the clause doesn't restrict or limit the noun it modifies (Old Professor Legree). The commas signify that the adjective clause provides added, not essential, information.

Other examples:
Edgar Allan Poe, who wrote "The Raven," is a great American poet.
Puerto Rico was a Spanish colony until 1898, when it was ceded to the United States.

Restrictive Adjective Clauses
A restrictive modifying clause (or essential clause) is an adjective clause that is essential to the meaning of a sentence because it limits the thing it refers to. The meaning of the sentence would change if the clause were deleted. Because restrictive clauses are essential, they are not set off by commas.

Here's a example:
An older person who dresses like a teenager is often an object of ridicule.

Here, the adjective clause restricts or limits the meaning of the noun it modifies (An older person). A restrictive adjective clause is not set off by commas.

Other examples:
All students who do their work should pass easily.
The car that I want is out of my price range.
The gas company will discontinue our service unless we pay our bills by Friday.
So let's keep in mind two basic rules:
Nonrestrictive
An adjective clause that can be omitted from a sentence without affecting the basic meaning of the sentence should be set off by commas.
Restrictive
An adjective clause that cannot be omitted from a sentence without affecting the basic meaning of the sentence should not be set off by commas.

taken from:
http://www.cws.illinois.edu/workshop/writers/restrictiveclauses/