The Trading Center allows a player trade what they have for other items. It can be anything such as Stamina, Sapphires, Arena Coins, Brawler Badges, Pets and Gems. The trading center may be extremely useful for players have a lot of excess of something (such as Stamina) and not a lot of time to actually use it. By trading in the excess you will be able to maximise your efficiency and make the most of what you have.
For example: Trading 50 Stamina and 50,000 gold for 5 Sapphires which can be used in monster wave. 50,000 gold is easily made up by using 1 or 2 Sapphires so you are actually getting benefit off from trading in the excess Stamina.