This is so important that it gets its own chapter. There are many chess books written on this topic, and paying attention to threats may be the biggest difference between strong and weak players.

Very simply, if you don't notice that your queen is in danger when you make your move, you might lose her. If you don't notice that you can checkmate you opponent's king in two moves, you may not go on to win the game. If you don't notice that your king is about to come under attack, you may not be able to find a good defense.

If this sounds like you have to pay close attention to possible threats on every move of every game, that's because it is the only way to become a strong player. Sherlock Holmes, with his excellent eye for minute detail and his awareness of clues that everyone could see but few could interpret, would have made a strong chess player.