Inbox Zero means what it says: nothing what so ever is left in your in box.
It also means that emails are processed to the point where you'll never have to read them again.
Processing emails involves either:
- just deleting them
- actioning them immediately
- adding items to your todo list
- adding their contents to your reference database.
Some emails don't even need to be read once - they just need to be deleted. Spam, for example.
There is no value in a "read" items folder. Once an email has been processed, it should be deleted.
A little more research shows that what I've written above isn't actually correct.
According to http://inboxzero.com/ the term "Inbox Zero" originates with Merlin Mann. The site explains that "Inbox Zero" is "not how many messages are in your inbox – it’s how much of your own brain is in that inbox. Especially when you don’t want it to be. That’s it.".