If, during your turn, you won at least one territory, you will be awarded a card. There are three types of card, distinguished by their design and colour. At the start of your next round, if you can make a set of three of the same type, or one of each, you may trade that set for extra armies. If you have five cards you must trade a set - otherwise it is optional.
The number of armies that a traded set is worth increases for each set that any player trades - so it may be advantageous to defer trading a set until subsequent rounds.