BackWeb is a process associated with an application from Backweb Technologies. It comes bundled with other products and is used to detect and download available updates.
For an explanation of BackWeb, http://www.cexx.org/dlgli.htm
Another thing you may want to check for: go to Add Remove programs. If you see Logitech Desktop Messenger, you can delete it. It's not critical to the use of your Logitech product. All it does is supposedly inform you of updates for your product.