Use commas around a “nonessential clause,” which is material that is extra information and does not change the meaning of the sentence when taken out.
My brother, who is single, lives in New York City. (nonessential)
My brother who is single lives in New York City. (essential) (why?)
Does this mean it's your choice whether you think the information is essential or non-essential? What is the difference between this usage and the below example which states the indentifier of the sentence may prompt the usage of commas.
If the parenthetical element in the sentence is closely identified with the subject the comma may not be necessary.
His wife Jill was a high flyer in the city.
Jill, his wife, was a high flyer in the city.