Use a comma if the additional information is not part of the main statement.
Note:
Depending on the importance attached to it, additional information can be enclosed in brackets, commas or dashes.
Brackets – not important
Connor (Amy's boyfriend) bought the tickets.
Commas – neutral
Connor, Amy's boyfriend, bought the tickets.
Dashes – emphasised
Connor–Amy's boyfriend–bought the tickets.
Use a comma in relative clauses before who and which if the information is not essential for the understanding of the sentence.
Example: Her brother, who lives in Chicago, came to see her.
Don’t use a comma in relative clauses if the information is essential for the understanding of the sentence.
Example: Her brother who lives in Chicago came to see her.
Don’t use a comma if the relative clause starts with that.
Example: The book that I’m reading now is interesting.