If you want to completely nuke a Dropbox account and the files in it, there are actually quite a few steps involved, as I explained in How do I delete Dropbox (which also appears in the "Rogue FAQ" at the end of the book).
Here's the crux of the issue: While it is possible to delete or "permanently delete" individual files from the Dropbox website, "deleting" the Dropbox account on the website or deleting the Dropbox app on your computer does not delete files on the computer or any other computer/mobile device on which they are stored.
Dropbox explains the situation with deleted accounts like this:
Deleting your account will delete your account from the website. Your computers will no longer sync with the website or to other computers or devices. However, canceling will not remove the files in the Dropbox folder on your hard drive or the hard drive of other members of shared folders you've created.
As for deleting the app on your computer, I tried this and discovered that the files in the Dropbox folder just stayed where they were.
So how can you delete everything? I explain how in the Rogue FAQ (linked above), but be warned: It's a long, convoluted process.