While automated backups are important, sometimes you just want to take a quick and dirty MySQL Backup of a database or all databases before making a change to your data. When changing files in Linux, you can simply cp a file to another name, and cp it back if your change does not work out. With MySQL, it is not quite that simple, but it is by no means difficult.
The mysqldump command is used to create textfile "dumps" of databases managed by MySQL. These dumps are just files with all the SQL commands needed to recreate the database from scratch.
Since the dump files are just SQL commands, you can restore the database backup by telling mysql to run the commands in it and put the data into the proper database.
There is no special wisdom to pass on to you regarding restoring databases from cPanel backups. If you do not wish to use cPanel's automatic methods of restoring entire accounts, you can open up the individual backup on the command line, find the mysql dump file you wish to restore, and use the above commands to perform the restore.