From the publisher:
In Colosseum, players are empresarios, trying to put on grander and more spectacular shows to draw bigger audiences and nobles to their amphitheater. At the end of the game, the player who put on the single biggest show will be declared the winner.
During the game, players will purchase show programs or amphitheater improvements, take turns initiating bidding on sets of 3 show assets, move nobles around the board, and then put on shows using their assets to score points and earn money. Each round, the player who put on the biggest show will earn bonuses for later, but at the end of the game, only your single biggest show during the game counts for your final score.