What makes King’s Court-King’s Court-Goons-Goons-Masquerade so powerful?
The combo is what is known as a "pin", although the biggest problem with it has been somewhat fixed in the 2nd version of Intrigue, which changed how Masquerade works.

For reference, the three cards are (using their 1st edition wordings):


  King's Court: You may choose an Action card in your hand. Play it three times.
  
  Goons: +1 Buy. +$2. Each other player discards down to 3 cards in hand.
  While this is in play, when you buy a card, +1VP.
  
  Masquerade: +2 Cards. Each player passes a card from his hand to the left at once. Then you may trash a card from your hand.


This only works in two-player games. First, you get yourself to a point where your deck consists solely of 2xKing's Court, 1xGoons, 1xMasquerade. Then:

Play a King's Court
  Choose King's Court
  Play King's Court (1st time)
    Choose Goons
    Play Goons 3 times (opponent discards down to 3 cards)
  Play King's Court (2nd time)
    Choose Masquerade
    Play Masquerade (1st time)
      You have no cards to pass
      Opponent passes you a card
      Trash the card
    Play Masquerade (2nd time)
      You have no cards to pass
      Opponent passes you a card
      Trash the card
    Play Masquerade (3rd time)
      You have no cards to pass
      Opponent passes you a card
      Trash the card


Note that playing Goons means they only have 3 cards in hand when you play the Masquerade, so you wind up trashing all of the cards they are holding and they start their turn with an empty hand. At some point, you end up trashing your opponent's entire deck, leaving them unable to do anything but purchase Coppers and Curses. You can choose to push the game to end by buying a couple of Estates (which will net you Goons points, and you can then pass the Estate to the opponent, get it passed back, and trash it) or just leave your opponent powerless and incredibly annoyed.