La Conciergerie had three different towers (from the remnants). They were the Silver Tower, which housed royal treasury; then the Ceasar Tower, which was for Roman empires; and the Bonbec Tower, which was used as a torture chamber.
The importance of La Conciergerie was to hold prisoners during the French Revolution, it also held the Revolutionary Tribunal and after the French Revolution it held, what the French called, important prisoners.