Comma Rule: Use a Comma to Separate Nonrestrictive Elements

Nonrestrictive elements are clauses that do not affect the fundamental meaning of a sentence. They provide information that is not necessary to the basic idea of the sentence.

Correct
Chudley, who is passionate about pigeons, lives on the roof of my building.
I had a dream that Barack Obama, who is the president of the United States, was disappointed in my grades.
“Who is passionate about pigeons” and “who is the president of the United States” are not essential information to the success of the sentence. Instead, they add details that the sentence doesn’t necessarily need. 

Oh jeez. He’s flashing his “I’m disappointed in your performance at school” smile.

Incorrect
Danbo the famous baker lost a thumb in a terrible egg beater accident.
Estelle who considered internet browsing aberrant behavior wrote letters to all her grandchildren via carrier pigeon.
To correct these sentences you would put commas around “the famous baker” and “who considered internet browsing aberrant behavior” because those two bits of information are nonessential to the meaning of the sentence. 

Pictured above: the last time he ever made that gesture.