How do you give/set folder permissions for individual website users - does all access flow through a single local NT User account?

Okay, I am trying to understand how I can give each user of my website permissions to a single personal folder on the server machine. I am really confused about how to do this since all website users accessing my server are basically running under 1 NT account name anyway. For instance, all users accessing my website server are generally doing it through a single NT user account named "DefaultAppPool". So I can give "DefaultAppPool" permissions to a private folder by way of a call to System.Security.AccessControl.DirectorySecurity.SetAccessRule() but I can't pass the Request.LogonUserIdentity.Name property because that will be the same each time no matter what the actual logged in user name is. And I can't pass the actual logged in user name because that will never be an NT user account.
Can someone please point me in the right direction on how to go about offering folder permissions on a per user basis? Thanks for reading.