There are two main types of brackets.
Round brackets (also called parentheses) are mainly used to separate off information that isn’t essential to the meaning of the rest of the sentence. If you removed the bracketed material the sentence would still make perfectly good sense. For example:
Mount Everest (8,848 m) is the highest mountain in the world.
There are several books on the subject (see page 120).
He coined the term ‘hypnotism’ (from the Greek word hypnos meaning ‘sleep’) and practised it frequently.
They can also be used to enclose a comment by the person writing:
He’d clearly had too much to drink (not that I blamed him).
Square brackets are mainly used to enclose words added by someone other than the original writer or speaker, typically in order to clarify the situation:
He [the police officer] can’t prove they did it.
If round or square brackets are used at the end of a sentence, the full stop should be placed outside the closing bracket:
They eventually decided to settle in the United States (Debbie’s home).