In a 13 card game, a player on his/her turn is supposed to pick up the 14th card (either from the draw pile of the discard pile); use the 14th card if required and then discard the 14th card.
The discarded card could be the card he just picked or any card from his existing 13 cards. The player should have 13 cards at the end of his/her turn.
The cards that are discarded by the players form the discard pile. Some people also call discarding a card as laying off a card.