The activation code doesn't work.
To activate Final Cut Library Manager, Final Cut Library Opener or VideoTweet you simply need to click on the link in the email that you've received. It's a link which will open your browser, then automatically add your code to the installed software.
If that doesn't work, copy the code and paste it into the "Licence..." window. Ensure that you don't add extraneous spaces to either end.
If this still isn't working then please try restarting the appliation.