Parentheses () - In most cases, you will see additional information in parentheses. Usually, it can be omitted without creating any confusion for the reader.
For example:
My young daughters (aged 5 and 7) just love playing with our neighbors’ dogs.
Brackets [] - Brackets are, in a way, similar to parentheses. However, they are mostly used in academic writing and when presenting quotes. For instance, the writer can add extra information or fix mistakes in brackets, without changing the original quotation.
For example:
The witness said, “I could hear him [the policeman] but I couldn’t see him”.