To export your database, you will need to open it via phpMyAdmin first.
On phpMyAdmin, press Export:
If you want to simply export to SQL file (SQL file is everything you need when moving databases), just click on Go:
Also, if you wish to set special requirements, you can change the format or choose to export only some tables from your database:
That’s it! Once you click Go a copy of your database will be downloaded to your computer. In case export failed - try exporting your database via SSH.