dropboxsynchronization
I have a folder named MyFolder in the Web-Dropbox. I downloaded the desktop version of Dropbox and installed it. The Desktop-Dropbox folder contains a folder named MyFolder but its contents are not identical to the contents in the folder of the Web-Desktop.
What will happen?
In the web interface click repeatedly the second column header, i.e. Type until it shows Size - then you will see the size of all the items in the current folder.
In the latest version it is now a drop-down that you can click and select Size.
Dropbox uses a binary diff algorythm to break down all files into blocks, and only upload blocks that it doesn't already have in the cloud. All of this is done locally on your computer.
Dropbox doesn't just use your files that you have already uploaded, it aggregates everyones files into one database of blocks, and checks each local block hash against that database.
This means that if someone else has uploaded the same file as yourself (say for example, the latest Ubuntu iso), then the upload will seem instant as there is nothing to upload, but if you are updating a file that changes regularly, like your backup file, then only the changes are uploaded. If you upload a totally unique file, then you have to wait for it all to upload.
Best Answer
Both folders will end up with the same contents. Whatever is on your desktop and not on the Web will be sync'd to the Web, and vice versa. If there are any files with identical filenames Dropbox will try to determine which is the one it should keep. I don't know the details of their algorithm but I would think they would keep the one with the newest timestamp. (Then again, Dropbox often gets very cautious if it can't tell and will keep both files with modified filenames to indicate a conflict.)
This would be really easy to test.