The combo deck is a bit of an unknown quantity in the world of Hearthstone. They can very rarely be found in ladder games but it is still a type of deck which has its own characteristics. You'll often need a lot of time and a good dose of experience to be able to master all the possibilities offered with a combo deck.
No need to know the deck played by your opponent because it is the success of your combos that will give you your advantage. The combo decks are composed of cards which work well together and have a spectacular result. The effect can be fun because your opponent could be put in difficulty in a well traded turn.
The weakness of this deck comes from needing to have at least two cards in your hand that are likely to be combined. So you will need a bit of luck in your starting hand as well as when you draw. Most of the time, you'll quickly know if you will be able to win the game. This is an "All-in" deck, and if you don't get the right cards, the game will quickly be over!
The most obvious example of the combo deck is no doubt the Miracle Rogue Deck. It allows you to play a huge amount of cards that work together in the same turn. If luck and talent are with you, one turn will be enough to overcome your opponent. The combo decks are often very fun to play, but aren't the most reliable.