“The writer who neglects punctuation, or mispunctuates, is liable to be misunderstood.... For the want of merely a comma, it often occurs that an axiom appears a paradox, or that a sarcasm is converted into a sermonoid.”
— Edgar Allan Poe, “Marginalia,” Graham’s Magazine, Feb. 1848 —

BRACKETS

You can use brackets to include explanatory words or phrases within quoted language:
Lew Perkins, the Director of Athletic Programs, said, “Pumita Espinoza, the new soccer coach [at Notre Dame Academy] is going to be a real winner.”

If you are quoting material and you’ve had to change the capitalization of a word or change a pronoun to make the material fit into your sentence, enclose that changed letter or word(s) within brackets:
Espinoza charged her former employer with “falsification of [her] coaching record.”

Also within quotations, you could enclose [sic] within brackets to show that misspelled words or inappropriately used words are not your own typos or blunders but are part of an accurately rendered quotation:
Reporters found three mispelings [sic] in the report.

You can use brackets to include parenthetical material inside parenthetical material:
Chernwell was poet laureate of Bermuda, (a largely honorary position [unpaid]), for 10 years.

— Capital Community College Foundation
Guide to Grammar and Writing —

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.”

— Lynch, Guide to Grammar and Style —