Just as you might have to omit something from quoted material with ellipses, you sometimes have to add to a quotation to clarify it. A sentence with only a pronoun like he or she, without the context of the surrounding sentences, might baffle a reader. Or a word or phrase may need explanation — say, a passage in a foreign language.
In these cases, it's traditional to add material in [square brackets]. (Newspapers often use parentheses instead of square brackets, but they're a minority.) Provide an explanation if the author uses something your audience isn't likely to understand — "The first words of Joyce's 'Stately, plump Buck Mulligan' are Introibo ad altare dei ['I will go to the altar of God']." You might need to supply a detail not in the original quotation, especially if your reader is likely to be confused: "As Fairbanks notes, 'The death of three civil rights workers in Philadelphia [Mississippi] marked a turning point.'" You might also provide a first name: "It was [George] Eliot's most successful work." Always the question is whether the clarification will help your audience.
If you're changing a single word or a short phrase, especially a pronoun, and the word isn't especially interesting in its own right, it's okay to omit the original and replace it with the bracketed interpolation: you can change "In that year, after much deliberation, he issued the Emancipation Proclamation" to "In [1862], after much deliberation, [Lincoln] issued the Emancipation Proclamation." If you're hesitant to monkey with words in the original that may be important — and it's wise to be circumspect — just add the bracketed interpolation after the thing you're explaining: "The sixteenth president [Lincoln] abolished slavery."
You can also use brackets around part of a word to indicate necessary changes in its form. So, for instance, you might write, "In his brilliant Guide to Grammar and Style, Lynch provides sage advice on 'us[ing] brackets around part of a word.'"
Some house styles call for brackets to indicate changes of upper- and lowercase letters at the beginning of a quotation: "[L]ike this." I don't like it — it clutters a page — but I don't get to make the call, except in things I edit.
Limit square brackets to quotations of others' words. If you need to clarify something in your own prose, use parentheses (as I do here).
