Improve DropBox Security using Google’s Authenticator App on the iPhone
This method will prevent someone from using your DropBox account without your permission–even if they have your account password. Use it to grant access to only those computers that you authorise.
Once it’s configured and you attempt to sign in to www.dropbox.com with a new device it will present this dialog:
To go any further you’ll need to open the Google Authenticator app on your iPhone and get a 6-digit Code. Note: ticking the option to ‘Trust this computer’ will allow access until you unlink the device in the account security settings.
The setup procedure is fully described here: https://www.dropbox.com/help/363/en