The door card is a poker term usually associated with stud poker games. It refers to the first upcard dealt to the players. In five-card stud that would be the second card dealt, but the most typical version of stud is seven-card in which case it refers to the third card dealt. In community card games such as Omaha and Hold'em the door card is the first exposed card on the flop.
There is definitely something to the theory that the door card has more of an impact on a number of players than the other two cards dealt on the flop. If a player holds an Ace and the door card is an Ace, as opposed to say the third community card, he becomes more committed to the hand. It's that little adrenaline rush of seeing the Ace first that triggers the idea that the hand is a good one.
The same theory holds true for hole cards. If you see a 2 followed by an A you are generally not as bullish about the hand as you would be if you saw an A followed by a 2. The sense of expectation can lead to heavy losses in poker, and if all else fails why not blame the poor door card for your woes?