I am pretty sure Explorer uses the API allowed by Apple and it just stays open so other running programs can utlize it when run in the background.
I'm not sure why all developers don't add this function by default.
Here is the info straight from Apple:
Support for External Displays and Projectors
An iPad can now be connected to an external display through a supported cable. Applications can use this connection to present content in addition to the content on the device’s main screen. Depending on the cable, you can output content at up to a 720p (1280 x 720) resolution. A resolution of 1024 by 768 resolution may also be available if you prefer to use that aspect ratio.
To display content on an external display, do the following:
Use the screens class method of the UIScreen class to determine if an external display is available.
If an external screen is available, get the screen object and look at the values in its availableModes property. This property contains the configurations supported by the screen.
Select the UIScreenMode object corresponding to the desired resolution and assign it to the currentMode property of the screen object.
Create a new window object (UIWindow) to display your content.
Assign the screen object to the screen property of your new window.
Configure the window (by adding views or setting up your OpenGL ES rendering context).
Show the window.