Discard is taking a card from your hand and placing it into your graveyard.
When making an opponent discard, many effects discard cards at random, but some let the player who will be discarding decide which card to lose, while some even let the effect's controller decide on the card for the opponent by first revealing the opponent's hand. Usually the latter effect is the most expensive option in terms of raw mana cost, and the former two effects are lower in mana cost.
Since Duel Masters allows for hand refilling as a part of making progress towards ending the game due to its shield-breaking aspect, discard can be a potent strategy to counteracting the additional cards gained by a player whose shields were broken.
To counteract the potency of discard in Duel Masters, some cards actually gain benefits or protection from being discarded or otherwise turning the typically negative effect into positive gain, for example Berlin, Bell Gravekeeper and [card that cannot be discarded].
God ● Metagame ● Multicolored ● Vanilla