As the screenshots included in this post show, the Remote application on the iPod Touch or iPhone does more than just meet the same capabilities offered by Apple's miniscule white remote. Benefitting from the wide touchscreen, I can browse thousands of songs, albums and artists quickly, and see a mirror image of what's playing on my Apple TV, letting me change the song with a single tap of my finger, anywhere in range of the Airport wireless network that both my device and the Apple TV share.
In contrast, the white remote has always been painstakingly slow to browse large libraries, practically forcing an indent into my thumb as I held the down key just to pass the letter "M". Given my library has almost 6,000 songs on it, and 23.6 days worth of music, that can be a frequent problem.
Once the Remote application is synched up with your Apple TV, using it is very simple. Choose "Playlists", "Albums", "Artists", or search for a song or any band. Unlike the white remote, you can actually type on your iPod Touch or iPhone, making this very quick.
Now, instead of relying on my iTunes on the laptop, and just turning up the sound to full blast, or resigning myself to not listening to my music as I move around the house, I can leverage the sound system on my TV set, and play DJ from room to room. I can even go to the "More" tab and select what the Apple TV was always intended to do - play movies and TV shows. But overnight, this little would-be useless application has become a must-have. I'm not leaving my iPod Touch laying around any more.