The ATV2 supports Netflix, MLB.TV, NBA, vimeo, and a few others natively not supported by the ATV1. Plus it handles higher quality HD formats and the home sharing support works far better than the streaming did on the ATV1.
In Apple TV iOS5 beta, they added iCloud Photostream support so you can take a picture on your phone and it is immediately available on the ATV2 without needed to upload, sync, or anything. A recent update also enabled you to access and stream any TV shows that you ever purchased from iTunes directly from the iCloud.
But that's just a small part of what the ATV2 supports that the ATV1 doesn't. The biggest difference in my opinion is Airplay. There are literally thousands of iOS apps that work on the ATV2 through video Airplay with more being added all the time. All apps support audio Airplay. And with iOS5 your entire device mirrors with Airplay whether the app supports Airplay or not and Apple enabled Airplay to work with any website by default so that any web video that you can watch on your iOS device you can now watch on your TV.
Apple's direction seems to be that you browse and select content on the very nice multitouch device in your hand (since it is much easier to do than using a remote) and then just use the TV as a "dumb" display device. The cool thing is you can still use the remote for playback controls after the video starts playing which is the one thing a remote is better for. It's a really nice system.