Brackets in a phone number typically are used to show a part of the phone number that is different from other parts of the phone number.
Although they are never entered in the call sequence, their purpose can vary by country.
North American Numbering Plan countries
In the countries of the North American Numbering Plan (Canada, the United States, most Caribbean territories, and U.S. territories in the Pacific), brackets are used to hilight the area (geographic) code part of the phone number.
When calling from another country, the geographic code is always included in the call sequence.
Even when dialing locally, especially in urban areas with multiple area codes, the geographic code is included as well. It is only in areas with 7 digit local dialing that it is not included.
Rest of the world
Outside of the North American Numbering Plan, brackets in a phone number can mean:
Around a ‘0’
When brackets are around a zero, it typically signifies that the zero is a long distance trunk number – that it is dropped when calling from another country (as is the case for most countries with trunk number ‘0’ except Italy, San Marino, and Vatican City where the ‘0’ is kept in the call sequence).
Around a country code
When there are brackets around a country code, they are there to hilight the country code.
When dialing domestically, the country code is not included in the call sequence.