We use the square bracket mainly within a quotation, to help our readers understand the quote by inserting words of our own. This lesson shows several instances in which you might find this device helpful, and how to properly use it.
Source: Linda Neuman, http://grammar.ccc.commnet.edu/grammar/marks/ellipsis.htm#brackets, http://grammar.ccc.commnet.edu/grammar/marks/ellipsis.htm#brackets