I was just reading this https://en.wikipedia.org/wiki/Clustered_file_system#Distributed_file_systems
The definition of a DFS seems to exactly describe Dropbox to me but it isn't in the list of examples, which of course it would be if it was one I think.
So what is different about Dropbox which makes it not fall into this category?
Usually, when talking about distributed file-systems, you expect properties that Dropbox doesn't support. For example, if you and I share a folder, I can create a file called "work.txt" in it and you can create a file "work.txt" in it, and if we do it fast enough (or when we're not syncing with dropbox) we'll have conflicting copies of the same file.
A similar example would be if we both edit the same file concurrently - we'll have conflicting copies, which is something a distributed file system should prevent. In the link you refer to, this is called "Concurrency transparency; all clients have the same view of the state of the file system".
Another example of a property dropbox doesn't support: if my computer fails (e.g., my hard-drive is corrupted) I might lose data that wasn't uploaded to Dropbox. There is a small window in which I think my data was written to the local disk, but if my computer fails, I lose that data.
Lastly, I'm not sure how Dropbox will operate with file locks. For example, MS office takes locks on .doc files, to ensure no one else is working on them at the same time. I don't think Dropbox supports this feature.
I've written a blog post about some of complexities of implementing a distributed file-system, you might find it helpful as well.