Exporting database
Connect to your cPanel;
Access the phpMyAdmin menu under the "Database" section;
Select the database you want to export on the left menu(list of the databases);
When the selected database is open, use the top bar menu and select the "Export" button;
On the next menu, you can basically use the default options(Quick method and SQL format);
If everything is fine, press "Go" and the database in the .sql file will be downloaded.
Importing database
Connect to your cPanel;
Access the phpMyAdmin menu under the "Database" section;
Select the database you want to export on the left menu(list of the databases);
When the selected database is open, use the top bar menu and select the "Import" button;
You will need to press the "Browse" button and select the previously generated .sql file of your database backup;
Make sure to review the general settings on this page, the character set, format. If everything is okay, press "Go"
Depending on the database size, internet connection it might be an instant upload or it may take some time. When the database is imported(uploaded), you will see the confirmation message, like below:
Note. If you are moving database information within the same server(or provider), in most cases you don't need to pay much attention to charset, as this parameter will most likely be the same. However, if you are moving the database file within different providers, you should keep in mind that the configuration of these servers could be different, and just check the charset so it would match.