The big time is the top: the place where you are famous or important enough that many people know your name. People say it most about films, music, sport, and shows — a singer who fills a hall, an actor on the big screen — but you will hear it in politics and business too. It is informal. A magazine might write that someone has hit the big time; a law paper would not. You often meet it in set phrases: hit the big time, make it to the big time, a big-time star. Though actually the same spelling also turns up in speech as a way of saying “very much” or “in a big way” (that hurt big-time), which is a stretch of the same idea, not this sense. The hyphen is common when it sits in front of a noun; as a name for that top level, many people still write the big time as two words.