The Windows.System namespace provides the Launcher class which exposes the method LaunchUriAsync which can be used to launch the Web Browser and navigate to the external Uri as described below.
Launch URL in Web Browser using LaunchUriAsync in Windows Phone 8
Below is a sample code snippet demonstrating how to Launch URL in Web Browser using LaunchUriAsync in Windows Phone 8
async private void Button_Click_1(object sender, RoutedEventArgs e)
{
await Launcher.LaunchUriAsync(new Uri("http://www.abundantcode.com"));
}