What does it mean when you see square brackets around a word in an newspaper article?

Square brackets are usually used when a portion of what someone said is being quoted, but an absolutely literal quote of the passage would lack context. The speaker may have referred to something or someone by name in a previous sentence, but in the sentence being quoted the speaker had used 'it' or 'she' instead of repeating the name. For example, the speaker, Joe Blow, may have said, "Jane Doe is running for mayor of North Podunkville. I have known her for many years. She is a fine citizen and an honest politician. She has my enthusiastic support. I have no hesitation in saying that she will be the best mayor North Podunkville ever had." Newspapers have limited space and must edit very tightly. The article might simply read, "[Jane Doe] will be the best mayor North Podunkville ever had," said Blow.