The 'Inbox Zero' theory is part of the GTD task management framework (Which I have been dabbling in for the past few years).

An email inbox is effectively a collection of tasks allocated to you by other people. The tasks can generally be divided into three categories.

1. The ones you don't need to action (eg Junk mail, newsletters)
2. The ones you do need to action (eg Emails from friends, clients)
3. The ones you need to archive for future reference (eg Receipts)

However, leaving all of the kinds of tasks jumbled together in the inbox, which most people do, is bad management. It's akin to leaving all of your mail piling up on the table after reading it. Each email in your inbox unnecessarily draws your attention as you know you might have to do something with it, but haven't committed to anything, and the unimportant items obscure the important ones.

Fortunately, Gmail offers some great tools for achieving Inbox Zero. This is how I manage it.

First off, go to the Google Labs section and enable the 'Send and Archive' button.

Now, process your mailbox. This should ideally be done at least once a day:
 

1. Read the first item in your inbox.
2. Do you really need to do anything with it? If not, delete it immediately.
3. If you want to keep it for future reference and like using labels, label it now.
4. If the email requires an action and you have time, do so and then click Archive (Or 'Send and Archive' if you reply).
5. If you don't have time to do what the email requires, "Star" the email, and then click Archive.
6. Repeat until your inbox is empty.

All done. You now have a freshly cleaned, good-as-new inbox again. The starred folder has now become a list of actions that you have committed to doing, so make sure you return to there when you have time to deal with them.

There is also an added bonus for having an empty inbox: Gmail conveniently provides a link to Google Reader in the empty space.