A discard pile is a pile where used cards are placed. Each deck of cards (Cosmic, Reward, and Destiny) has its own separate discard pile. If any deck runs out of cards, the cards in its discard pile are shuffled to create a new deck.
At the end of each encounter, the played encounter cards are put into the discard pile (first the offense's card, then the defense's). Used artifacts, reinforcements, and rifts are placed in the discard pile after their effect is finished.
While the front faces of cards from the cosmic deck and reward deck look the same, the backs are different, so make sure not to mix them up.
The destiny deck has its own discard pile. Drawn destiny cards are placed in the destiny discard pile.