Metro style apps are the new type of applications that work with Windows 8 (and future operating systems from Microsoft).
Metro style apps function similar to the traditional Windows apps in terms of end user experience. However, there are significant difference in the way they are developed since the way Metro apps interact with Windows OS and other apps are different from traditional apps.
Metro style apps are represented by "Tiles" in the Windows metro start screen. You can launch the app by clicking the Tile on the Windows.
There is no explicit "Close" for a Metro app. Instead, when you switch to other apps, the Metro app will automatically go back to a hidden state but it will be still running in the background with minimal memory, CPU and resource usage. Metro apps can continue interacting with Windows and peer apps even when it is in a hidden state.
The most important aspect of a Metro style app is, even when the app is not actively running, it can interact with the users and push updates through the Windows Tile that is visible in the Metro start screen.
Consider you have a Metro App for Weather information. The App can update the current weather info on the Windows Tile for the app so that the users can see the current Weather information without opening the app.
The Metro style apps are expected to provide a much better, interactive user experience for the end-users. Learn more about Metro Style Apps.