Four big things I've found so far:
1. You can post pics from your phone to the forum far faster, and they are automatically sized to fit the screen. No more downloading and resizing.
2. You can respond to topics much faster than going through the web on your phone.
3. You get alerts to your phone when a topic you're following gets a response. Could get annoying, but if you're waiting for an answer, could be helpful.
4. Less clicks to get into the forums via the app.