The iPad 2 will support full video mirroring with the Digital AV Adapter. This means that anything you see on the iPad 2 screen you will see on your HDMI connected HDTV or other device.
The original iPad also supports HDMI out, but without full video mirroring. Apple has restricted video out to the following list of applications on the original iPad:
Photos - Slideshow playback only
Safari - Video content on webpages