The finesse is sometimes hard to understand, but it's another way to develop extra tricks. It is available in either no trumps or suits. When a finesse is successful, it means you win a trick with a particular card (say the ♥Q), when the opponents hold a higher card (the ♥K). It depends on the way you play the suit, which hand you start the first play from, and which defender's hand holds the ♥K. So, a finesse works only half the time.
The principle of the finesse is to lead towards the card you hope will take a trick. Here are some examples where you are missing the ♥A but would like to take a trick with the ♥K.
If you need to win one trick in this suit, it won’t do any good to lead the ♥K, as the defenders hold the ♥A, and the ♥Q etc, and you'll lose to both these cards. It won’t help either to lead a low heart from the dummy since the defenders can win with one of the other high cards (e.g. the ♥Q), and retain the ♥A to capture the ♥K.
Instead, lead the ♥2 from declarer's hand towards dummy, and give yourself a 50% chance of winning a trick. When you lead the ♥2 first, the opponent on your left must play before you play from dummy. If they hold the ♥A, they can either play it, and you'll win with the ♥K next, or if they choose not to play the ♥A, you will play the ♥K now and win the trick.
Only lead a high card if you want the opponents to cover it. Otherwise, lead from the other hand towards your high card.
There are a few different forms of the finesse, but the basic technique is the same.