Brackets [ ] have very specific uses in formal writing; they are used either to insert commentary, denote errors in the original text, or indicate omitted words in a direct quotes.
Using Brackets
Insert Commentary
Campos states, "Of the two [people rescued from the rubble] only one was willing to talk to the press."
Errors in the Original Text
In his report, Taylor claims, "Only half of Americans use creamer in there [sic] coffee."
Omitted Words
Stampler argues, "There were no negotiations [...] only an outright refused to even come to the table."