Our Dropbox account contains many private files and some even store their passwords in it. With Google getting more secure with their 2-factor authentication system, Dropbox is doing something similar.
Dropbox has introduced two-step verification system which is an optional security feature you can enable on your account.
With this link you can enable it for your account, you account would have the option to enable the two-step verification. As soon you enable it, you would be guided through the process. The options avaible for two-step verification are as same as Google has, either SMS or Google Authenticator App. Dropbox too uses the Google Authenticator app for their added security, you just need to add another account to the App.
In case of emergency and not able to access the Authenticator app, Dropbox also gives you the emergency code which they as well as we recommend you to write on a piece of paper and keep.
So once enabled, the next time you try to access Dropbox via web or want to authorize any app to use your Dropbox account, you would be prompted to enter the code after signing in.
Read more about How to enable two-step verification.