The job fires and has no effect.
WHAT THIS USUALLY MEANS
The command runs and the script fails, or runs in the wrong context.
WRONG WORKING DIRECTORY
Cron does not run from your web directory.
A script expecting to find files relative to itself may not.
WRONG PHP VERSION
The script runs under a different version from your website and fails.
Specify the correct binary.
MISSING ENVIRONMENT
Scripts relying on environment variables set by the web server do not have them under cron.
PERMISSIONS
The script may not be readable or executable by the user cron runs as.
HOW TO SEE WHAT HAPPENED
Enable output by email, or redirect output to a log file.
The error will be there.
FOR WORDPRESS SPECIFICALLY
Check the HTTP method is actually disabled in wp-config.php.
If both are active, behaviour is confusing.