The official name for brackets is square brackets. In business writing, brackets are primarily used as parentheses within parentheses, for example, “Acme Technology decided to locate its headquarters in New York (the CEO’s home though other executives [two senior vice presidents] also live there) instead of San Francisco.”
Brackets are also used to enclose words added by someone other than the original writer or speaker: “According to her [the sales manager] the monthly quotas have been exceeded by 10 percent.”