Definition: A Roman triumph was more than a victory. The Senate (usually) decreed a triumph on the basis of a particularly important win and other criteria, for instance, the triumph was not supposed to be over Romans or slaves, but worthy foreign opponents. The general (a consul, praetor or dictator) ceremonially entered the city (originally Rome) with captives and booty paraded before him, and his troops behind him. The general himself rode a 4 white horse-drawn gilded chariot and then made a sacrifice to Jupiter (Jupiter Optimus Maximus) on the Capitoline. The general and his friends then enjoyed a public feast.
Examples:The Latin word for triumph is triumphus and the title of the general celebrating a triumph is triumphator.