Restrictive and non-restrictive clauses are also known as adjective clauses. They modify the noun which they follow. Restrictive noun clauses are essential to the meaning of the sentence. If they were eliminated, the meaning would change. However, non-restrictive clauses are not essential. They give additional information, but if omitted, the meaning of the sentence doesn't change. Here are examples of the two types of clauses where the first is restrictive and the second non-restrictive:
I have a sister who lives in Miami.
I have a sister, who lives in Miami.
Besides the difference in punctuation, the two sentences have different meanings. In the first sentence, the speaker has more than one sister, and one of his sisters lives in Miami. In the second sentence, he has only one sister, and she lives in Miami.
My brother whose name is Jack is a scientist.
My brother, whose name is Jack, is a scientist.
In the first example, the speaker has more than one brother, and one of them is named Jack. In the second example, the speaker has only one brother and his name is Jack.
Let's look at two more examples.
We had to wear a uniform which I didn't like.
We had to wear a uniform, which I didn't like.
The first sentence tells us that the speaker didn't like the uniform that she had to wear. In the second sentence, the speaker tells us that she had to wear a uniform, and she didn't like the policy. In other words, the speaker didn't like the uniform (sentence one) and the speaker didn't like having to wear a uniform. (sentence two)
Restrictive and non-restrictive clauses differ in meaning and punctuation. Restrictive clauses are essential to the meaning of the sentence and are thus never separated by commas. Non-restrictive clauses, on the other hand, provide extra information and are punctuated with commas.