The main function of square brackets [ ] is to make a quoted text more understandable or to align it within a new sentence. Square brackets are used to show that the text within is not the work of the original author. For example:
She said: "If I can't keep her [her horse], I'll scream the house down!"
(Here, the text in square brackets explains her.)
She said: "If I can't keep [my horse], I'll scream the house down!"
(Here, the text in square brackets replaces her.)
She "scream[ed] the house down" when they took her horse.
(Here, the text has been modified to fit the sentence structure.)
Using Square Brackets
Square brackets [ ] are usually used to make a quoted text more understandable.
Square Brackets to Make the Text Clearer
Square brackets are used to add information that explains the text it follows. (The information is usually added by someone other than the original author.) For example:
Hedy Lamarr once said: "Most people save all their lives and leave it [their money] to somebody else."
"It [electricity] is really just organized lightning."
Square Brackets to Modify the Original Text
Often, square brackets are used to replace text in a quote to make the quote clearer for the reader. For example:
Hedy Lamarr once said: "Most people save all their lives and leave [their money] to somebody else."
Alice Cooper famously said that "from the moment [he] leave[s] [his] house or hotel room, the public owns [him]."
Square Brackets: [sic]
The term "[sic]" is used to show that the word it follows featured in the original text. Often, "[sic]" is used to indicate that a grammar error in the text was written by the original author. For example:
The minister believed that his statement was "appropriate and did not undermine the moral [sic] of our troops."
(should be morale not moral)
Your demand for a "full compliment [sic] of men" cannot be met at this time.
(should be complement not compliment)
Square Brackets: [...]
Ellipsis is used to show text omitted from a quote. Ellipsis is usually written "..." or "[...]". For example:
It's no small irony that the government [...] ends up promoting precisely that which they would most like to repress.
(The word "inevitably and invariably" are replaced by the ellipsis.)
Andy Warhol is the only genius...with an IQ of 60.
(The ellipsis replaces the words "I've ever known" in this Gore Vidal quote.)
A Video on Using Square Brackets
Here is a video summarizing how to use square brackets: