In written English, brackets help to contain separate pieces of information. You can better understand the specific uses of this type of punctuation by reading this guide on how to use brackets.
Use brackets to make a clarification or a correction within a quote. The most common use for brackets is within quotes to clarify something another author has written. In this case, the information contained within the square brackets is not original to the quote - it is added by whoever is using the quote to further explain information within a quote. Here is an example:
"He [Santa Claus] dropped down the chimney with a bag full of presents."
In this example, Santa Claus isn't original to the quote but is necessary for the reader to understand the full meaning of the sentence. Here is another example of how to use square brackets within a quote to provide further explanation to the reader:
"She wore her bling [gaudy jewelry] to the school dance."
Similar to the first example, brackets are needed in order to insert non-original text that explains the wording in the quote.
You may also need to use brackets within a quote if you have to change the original capitalization in a quote. "He was a fast runner" must have the capitalization changed if it falls within another sentence as a quote, so to properly write it, one must put brackets around the changed capital letter. It would correctly appear like this:
When she saw Forrest Gump coming around the corner, she knew "[h]e was a fast runner".
Similarly, brackets are used to show a section of a quote that has not been included. If you wish to shorted a lengthy quote to include only the critical information you need to prove your point, use brackets around three periods (known as an ‘ellipsis') to show that a portion of the quote is missing. A shortened quote would look like this:
"I pledge allegiance to the flag of the United States of America, [...] one nation under God, [...] with liberty and justice for all."
The shortened quote must still make sense. But square brackets can be used to omit information.
Use brackets to add additional information to a sentence. Brackets are also used outside of quotation marks. In a normal sentence, brackets would be inserted to separate one piece of information from another. Usually, this piece of information is not crucial to the understanding of the sentence. Rather, it just provides further clarification, much like an ‘FYI' section for readers. For example, one might write:
I chose a chocolate sundae (without sprinkles) for dessert.
Notice how the information within the brackets isn't critical for understanding of the sentence. Rather, it just further explains the preceding part of the sentence.
Use brackets with parentheses when you want to separate more than one piece of information from the original sentence. Finally, brackets can also be used within each other in order to separate information from already-separated information. For example, when referring to a scene from a movie, it is common to see two sets of brackets within a sentence, looking something like this:
Brad Pitt's character is always faced with a struggle to overcome (as in Fight Club ) and he always seems to meet the challenge.
As mentioned, two sets of different brackets are used in this sentence to separate the year of the production of the movie from the movie title itself. Though less common, this is yet another acceptable way to use brackets.