Fig.: to abstain from drinking alcohol

Augustin is really a different man now that he's on the wagon. Before, he was drunk every night and he was a threat for himself and his family

Ora che Agostino ha smesso di bere è veramente un altro uomo. Prima era ubriaco tutte le sere ed era una minaccia per sé e per la sua famiglia

This expression originally sounded "to be on the water-cart", which was the horse-drawn cart used in the 19th century to wet down the dusty city streets. A heavy drinker who has sworn off alcohol, has climbed on the "water-cart", later called "water-wagon" and then shortened in "wagon"