It's probably easier to explain what organised is not!
Neat is not necessarily organised.
I have seen some very neat but disorganised workspaces. Everything looks good on the surface, but watch the scrambling when you ask for a specific file!
Lining up all your pencils just so means that you like your pencils all in a row, not necessarily that you're organised.
I think people confuse the looking good factor with being organised because when things look good, it's gives the same feeling that being organised gives you.
I've also seen people who work with piles but they can locate whatever they want very quickly. However, when these people get overwhelmed by the piles of paper, then it's time to go through them and reorganize.
Personally, when I'm working, I spread out a lot so I don't work in a very neat fashion. But I'm organised because all that spread-out paper relates to only my current project.
My definition of organised is being able to find something in a minute or less.
This is always my aim both personally, and when I work with clients. I want to create a system, working with their personalities, where they can find something within a minute or less.
So my question to you is this - can you find what you're looking for quickly? Are you neat, organised or both?