The hostname to use when connecting to one of your cPanel MySQL databases from a web script running within the same cPanel account is localhost.
As a quick guide, you can use the following PHP code to make a connection.
$hostname = "localhost"; // mysql hostname - always use localhost $database = "databasename"; // substitute your mysql database name $username = "username"; // substitute your mysql user name $password = "somethinghardtoguess"; // your mysql users's password $con = mysqli_connect($hostname, $username, $password) or die(mysql_error()); // make connection to mysql