A continuation bet continues your preflop aggression with a bet on the flop, regardless of the context of the flop. Most of the time if you raise with Ace Queen pre-flop you will miss the flop (around 70% of the time). With a continuation bet you are representing a monster hand such as Aces or Kings, and there is a good chance your opponent missed the flop and folds.
You are sitting in mid position with Ace Jack of spades and you decide to raise. Your opponent in late position calls your raise with 44. The flop comes Queen, Queen, King with no spades. You missed the flop but it is likely your opponent missed too. You decide to make a continuation bet and your opponent now has a decision to make. He decides to fold the best hand, because a King or a Queen fit easily in the range of hands you would raise.
The idea behind the continuation bet is to let your opponent not draw out on you or to let your opponent fold a better hand. It works even better if you have position on your opponents. However, some experienced players know what a continuation bet is and they will often call or raise your continuation bet. They might even do this if they don’t have a hand theirself, but they will try to take the pot on the turn if a blank comes up.
There are many factors to consider when to use the continuation bet. The player style of your opponent, is he capable of bluffraising a continuation bet, how likely he’s going to call and many more factors should be considered when making a continuation bet.