Web: Your Dropbox storage is limited, so you don't want to waste it on files that you won't need in the future. Finesse lets you schedule certain files in Dropbox to be deleted when you're done with them.
The web app is pretty straightforward. Pick the files you want to delete, set a date and time, and click "Schedule." When that time rolls around, Finesse will delete the files for you. This is especially handy if you're sharing files with someone and won't need them in a week, or want to clear out a folder when your projects are done.