Learner's definition of FAME
the condition of being known or recognized by many people
see also hall of fame
He died at the height of his fame.
The book tells the story of her sudden rise to fame.
He gained/found fame as an actor.
The house was once occupied by Noah Webster of dictionary fame. [=Noah Webster, who was famous for his dictionary]
achieving/earning/winning international/worldwide fame
She went to Hollywood seeking fame and fortune.