Brackets are used to insert explanations, corrections, clarifications, or comments into quoted material. Brackets are always used in pairs; you must have both an opening and a closing bracket. 

Do not confuse brackets [ ] with parentheses ( ). Parentheses are used to enclose additional information in your own writing; brackets are editorial marks used to insert comments into someone else's words that you are quoting, or to insert material into a passage already in parentheses.

Rules for using brackets [ ]

1. Use brackets to indicate you have inserted your own words into a quotation
   • Jim said, "She [Julie] finished the report last week."
   • "No more [government] equipment will be purchased for use in the facility," said Mark.
2. Use [sic] to show an error in a quotation
   Place the word “sic” (meaning "it is so" or "this is the way it was written") in brackets in a quotation to show that an error appeared in the original wording. If you want to correct the error, add the correction in brackets.
   • The note said, "telphone [sic] the hotel as soon as you arrive."
   • The candidate stated, "I grew up in Sacremento [Sacramento] in the 1960s."
3. Use brackets to insert information within parentheses.
   • While cleaning my closet, I found clothes I no longer wear (including pants, dresses [formal], and skirts). 
4. Use brackets to insert stage direction into a play.
   • [Macbeth enters]
   • [Romeo weeps over Juliet’s body]

How to use braces { }

Braces are used to group items or to show a relationship among lines, symbols, or formulas in mathematical, statistical, or chemical equations.