Discarding in draw poker games is the action of removing the cards from your hand in order to draw replacements from the deck. You can announce how many cards you want to discard, and these cards are thrown away into the discarded card pile.
Discard Poker Example:
In Five Card Draw poker, you can discard any number of hole cards and the dealer will give you the same amount of new cards. For instance, if you have a pair, you can discard the three unpaired cards and draw three new cards that will hopefully improve your hand.