I think background data is the process of an app syncing even when it is not opened.
For instance: Facebook app getting your messages/friend requests and alerting you via notification even when it's not opened.
or Twitter alerting you when you get a DM even when it's not opened.
If you have the background data UNCHECKED, your apps will NOT perform their syncs when unopened.
Everything that syncs will most likely be affected by this. FB, Twitter, Calendar, Mail, News, Weather, etc.