When a SharePoint 2010 Document is opened inside Word Client, it shows the properties of that document in a Document Information Panel. How does this work with Word Web App?
You do not have access to the DIP in Office Web Apps. Since you're using the web UI already it's easy to go the the item in the library and change it's properties there. If you need more advanced DIP's (for instance built with InfoPath) then you need to modify the edit, new and view forms of the page to get the "same" experience as in the full fledged Office client.