If you are configuring backup for the first time, the ID/Password you are being prompted for are your subscription LiveID for OneCare. Open OneCare and click Help/About to view the subscription LiveID.
If you have already configured backup and are being prompted for an ID/Password to do the backup, it is possible that you set up Centralized Backup and you need to provide the credentials for the shared location.
Another possibility is that you are not logged into the PC with administrator credentials, which were used when backup was configured.
If you need help with backup, you can post back here or contact support.
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator