To better understand the AppleScript, try breaking it down.
Within Script Editor.app run the following:
set outFolder to ((path to desktop from user domain) as string) & "PDF Files"
After running, the Result panel will show the value
outFolder is set to. This should be a path to a folder called
PDF Files on your Desktop.
Does this folder exist on your Mac? If not, this is probably the cause of the problems you are seeing.
The next line in the AppleScript tells the application Papers to export to that folder. If you have problems with Paper's AppleScript behaviour, do contact the developers; they will be best placed to help you.
Add a Try Block
You can add a try block around your AppleScripts. These will provide better error messages and hopefully catch problems.
Changing the Folder
You can add an interactive folder selection by replacing the
set outFolder… line to:
set outFolder to choose folder
Alternatively, change the "PDF Files" to the name of your preferred folder.