"Background Tasks" panel is used when you are exporting your document to PDF.
So you can open multiple documents, and export all of them to PDF without waiting for first to finish.
It's like PDF export queue.
Hope that helps.
In one case, that is, ID CS5 export doc as PDF file, one might be able to see the progress on the "Background Tasks" according to ID CS5 document. I am not sure whether my Plug-In background tasks can be shown on this panel or not.
I'm pretty sure it's only possible for tasks running in a separate thread...
You can also cancel a background task. Like when you hit export when you weren't quite ready...