The term 'BIG BALLS' can be broken down into three crossword solutions: PROMS (5 letters), GALAS (5 letters), and AUDACITY (8 letters). PROMS are formal dances held by high schools or colleges, usually at the end of the school year. GALAS are large, formal social events, often with a charitable purpose. Finally, AUDACITY is a quality of boldness or daring, often in the face of danger or difficulty. Together, these three words suggest a person who is willing to take risks and make bold decisions in order to achieve success.