Use the Full Backup feature / Full Home directory backup of cpanel , which will backup all the things like emails , databases , website files etc...Once the backup generation done you can simply download it to your local machine.
If you are with a shared hosting provider then you can simply ask the support to generate the full backup and emailed it to you. If you have your own server with cpanel then you can generate the full backup of the website account with command
To simply answer OP's question, yes, full backup does include MySQL database with files. Footnote being, the only one that can restore a cpanel full backup is your hosting provider or the one who has control to Webhosting Manager (WHM). So if you just want to quick backup that you can restore on your own, use partial backups of home directories and MySQL database instead. Both options are available through the backup wizard process.
Make sure you use the full account backup as this will include all files, databases, email, DNS information and everything else associated with the account.
cPanel also includes options to only backup databases/files etc.
cPanel full backup option back up everything on your cpanel like email, dns, subdomain etc.Use this feature.Keep in mind that you can't restore cpanel from cpanel using cpanel full backup.You have to use whm with root access.