The app allows you to send stuff directly from your browser to your phone, so if you find a link to something you want for your phone, you can send the page to your phone, open it up in your phone's browser and download whatever it is straight to your phone. Easier than downloading the file to your PC, then transferring it to your phone, or scanning a QR code.
The Chrome-to-Phone app can be found in the Market, and the extension for your browser can be found by Googling. Not sure how it works in Firefox, but in Chrome you just install the extension, and a Chrome-to-Phone button appears top right. Once you link your Google account to it, you just click this button to send anything to your phone.
A pretty cool addition to Android 2.2.