With Windows Phone you no longer have to manually close your applications. When you no longer need application, it stops running and remains the background for a certain period of time. This allows a quick re-opening of the application. However, it is still possible to completely close an application, especially if you want save battery life.
Windows Phone 7
For Windows Phone 7 (up to version 7.5) , you can close an application by holding the "Back" key for a couple of seconds.
Windows Phone 8
Windows Phone 8 fully integrates the concept of multitasking. Hold down the Back key for a couple of seconds to access the multitasking view. The list of recently used applications is displayed. When maximum number of opened application is reached, Windows Phone 8 will automatically close the least used ones. If you want to close an application, select it and hold down the Back key until the app closes.