When activated, iCloud automatically saves all of your Favorites and Notes in case a restore is needed at some future date. It also allows you to sync information between devices so that you will have access to your Favorites and Notes regardess which device you are using.
Unfortunately, Apple has not enabled iCloud to give users access to their app storage on iCloud.com. You will not be able to view your Favorites and Notes at iCloud.com. To learn more about iCloud visit the Help menu of iBird: More>Help>iCloud