I want to show from my application (iOS or Mobile Web Site if possible) the AppStore description page without opening the AppStore application, like facebook do. See images below for exemples:

==> Result

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This is a feature available in iOS 6. You should take a look at the SKStoreProductViewController class available in StoreKit framework.
According to docs in order to display an app store link within your app you will require an iTunes Product Identifier. For further reference please refer to aforementioned documentation.