Square Brackets are mainly used for indicating that some words have been excluded from a quotation or that words have been added and do not appear in the original quoted text. They are also used for clarifying information in a reference, and for avoiding nested round bracket parentheses.
Teachers [opening bracket...words omitted from original quotation]closing bracket need to learn how to deal with kids of different backgrounds. [opening bracket...words omitted from original quotation]closing bracket I suppose they need to further learn all the different cultures.(Adebayo 2023)
This is ellipsis See the glossary definition. The writer has used it in order quote a long piece of text (a block quote) but without including unnecessary material. Sometimes ellipsis is enclosed in round brackets and sometimes only the dots are used. You should consult a style manual See the glossary definition (APA, MLA, etc.) in order to decide which style you need in your text.
The original sentence was "Today, however, a multinational effort, under the auspices of the United Nations, is under way to cut the use of fossil fuels, based on the unproven theory that they affect the earth's climate" (Admin2 1996). The pronoun they refers to fossil fuels so the writer has replaced they with the original reference. If you quote text with a pronoun reference to something previously mentioned, you may have to use this technique to restore the reference and make the quotation make sense.
It would be useful to do fitness-type CPD [opening bracketcontinuous professional developmentexplanatory appositive]closing bracket , but we don’t really have the knowledge to share. We all go the gym, but what we can do with the pupils isn’t really clear.(Cox 2023)
The word "here" in the original spoken words could be ambiguous so the writer has clarified this: here means at school. But because this was not in the original words spoken, at school is enclosed in square brackets.
Square brackets are used in bibliographic references to indicate sources which are not typical text based sources. For example video (as in this example), social media posts, presentation slides, brochures, fact sheets.
You can see more information about the use of square brackets and other formatting information on this APA Style Guide.