Nancy,
it means that on your computer, you should lock it with your computer user account instead of logging out via unlinking. This is if you use the dropbox app on your computer.
One computer can have many computer user accounts.
If you are sharing your computer, you can create another computer user account for guests.
Files on the internet via www.dropbox.com must be logged in via your username and password before being accessed so no problems with that.
Logging out of Dropbox won't fix that. The files are still on your computer (as they were before Dropbox....). So, how did you secure them before Dropbox? Do the same now.