The idea of the Inbox Zero principle is to try and keep our inboxes clean. To do so, we need to regularly review our inboxes to avoid accumulating information there. We can also introduce automation in order to automatically clean the clutter.
Inbox zero helps keep a clear view over what remains to be processed/done, instead of having a huge pile of content that is hard to make sense of (i.e., a big pile of dirt or a big ball of mud). This helps avoid feeling overwhelmed and stay on top of things.
Inbox zero is generally associated with the email inbox, but it applies to all sorts of contents that need to be reviewed, processed, and organized. For instance, we can create an inbox folder for project documents, work to be done, fleeting notes in our Zettelkasten, etc. As such, this concept is also very useful for Personal Knowledge Management (PKM)
Inbox zero has been recommended by David Allen and discussed in his bestseller: Getting Things Done (GTD).