The main use of editorial brackets is in quotations, where they can be used to clarify information that you lose when you take the quotation out of its original context. Here’s a brief passage:

In June, 1992, the California Attorney General’s office accused the Sears Company of overcharging on automobile repairs. By way of excuse for their errors, Sears ran newspaper advertisements that stressed the huge number of repairs performed annually.

However, in your essay, you only want to quote the second sentence, where “their errors” has no clear definition. In order to do this, you could write the following: “By way of excuse for their [overcharging], Sears ran newspaper advertisements that stressed the huge number of repairs performed annually.”

The brackets let the reader know that while the word overcharging wasn’t specifically in the wording in the original quotation, you are confident that it was implied there.

Another use of brackets is when there is a spelling or informational error in the original quotation, as in, “To disengage gears, fist [sic] lock the mechanism.”  The term sic means that the typo was in the original source of this quotation. More technically, sic indicates that the reader should trust the accuracy of the quotation even though it looks like it contains an error; one obvious side effect is that if you insert sic, it shows that the error was the original writer’s doing, not yours.