Where Dropbox really shines is that they have an additional trick that badges the items in the Dropbox folder with their current sync status. However, I have no idea how it deals with merge conflicts (which could easily arise with one or more clients offline), which are not an issue if the server is the only copy and every edit changes that central copy. This setup has some decided advantages: it works when offline, it is an order of magnitude faster, and it is transparent to other apps, since they just see files on the disk. Going the other way, the Dropbox application watches for the files in the Dropbox folder, and when they change, it sends the appropriate deltas to the server, which propagates them to any other clients. Instead, only the deltas are sent over the wire, and the Dropbox application (running in the background) patches the files appropriately. It also means that the files don't need to be 'downloaded on every load,' since they are actually stored on my machine here. That's because the files are actually stored here on my hard drive. If I quit Dropbox (done via the menu item) and disconnect from the net, I can still use the files.
If it were powered by those things, it wouldn't work when you weren't connected, as both of those rely on the server to store the actual information and Dropbox does not. Dropbox is not powered by either MacFUSE or WebDAV, although those might be perfectly fine solutions for what you're trying to accomplish.
