You can backup your database two ways.
1. Click on Backup in Cpanel then click on the database name. This will download a gzipped copy to your computer.
2. Use the PHPMyAdmin feature in your control panel by clicking on MySQL and then phpmyadmin at the bottom. In PHPMyAdmin, select the database you want to backup and select "Export" tab on the right screen. Choose the tables you wish to backup (or "Select All" for all tables). Scroll down and tick "Save File As..." and click on the "Go" button. Simply save the database that begins to download, on your local computer.