「話「話{はなし}を大きく大{おお}きくする」 is a set phrase meaning "to stretch a story", "to exaggerate", etc.
The fine nuance intended is context-dependent, but the expression is most often used to describe how better, worse or more important someone is trying to make his story seem.
The common contemporary and colloquial version would be 「話を盛{も}る」.