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Those discards are called "burn cards." They're burned as a countermeasure to prevent cheating. If any of the cards are marked, the person who could read the marks would see the top card on the deck before it's dealt and while the dealer is holding the deck during the round of betting.
If a cheater knows which card is next to come, it gives him a significant advantage in strategy and betting. By burning the top card, it nullifies any advantage that could be gained by seeing marks on top of the deck, because it's actually the second card that gets put into play.