If you want to check the sync progress of your Dropbox, then click on the "Dropbox" icon located in the system tray or menu bar. When the rotating blue sync marker turns into a green check mark, then you will get to know the files and folders in your Dropbox are finished uploading/syncing.
If you want to see whether syncing process finished or not, then right-click the 'Dropbox' icon during syncing. You can see the Dropbox is uploading or downloading files. You can also monitor the transfer speed, the number of files remaining and the estimated time until completion.