There are two ways to export a database in cPanel:
Export Database via phpMyAdmin.
In your cPanel go to "phpMyAdmin":
Select a database to export:
Select the "Export" tab
Click "Go", and specify where to save the Database:
Export Database through Backup.
In your cPanel go to the "Backup":
Go to the “Download a MySQL Database Backup”, click on the DataBase's name you need and it will be saved on your local computer: