If you originally purchased Synergy Basic, and then purchased the Synergy Pro upgrade, you'll need to apply this update. You don't need to re-download Synergy, as you can simply upgrade your existing install.
1. Run Synergy
2. Click the File menu
3. Click the Activate menu item
4. Paste in your new serial key
5. Click the OK button
There you go, you're all set. You should now see Synergy Pro in the main window title, and your Synergy Pro features will work instantly.