WP_DEBUG is a PHP constant (a permanent global variable) that can be used to trigger the "debug" mode throughout WordPress. It is assumed to be false by default and is usually set to true in the wp-config.php file on development copies of WordPress.
For information on other debugging tools built into WordPress see Debugging in WordPress
define( 'WP_DEBUG', true );
define( 'WP_DEBUG', false );
WP_DEBUG_LOG and WP_DEBUG_DISPLAY are additional PHP constants that extend WP_DEBUG, and may also be used to debug WordPress.
WP_DEBUG_LOG is a companion to WP_DEBUG that causes all errors to also be saved to a debug.log log file inside the /wp-content/ directory. This is useful if you want to review all notices later or need to view notices generated off-screen (e.g. during an AJAX request or wp-cron run).
define( 'WP_DEBUG_LOG', true );
WP_DEBUG_DISPLAY is another companion to WP_DEBUG that controls whether debug messages are shown inside the HTML of pages or not. The default is 'true' which shows errors and warnings as they are generated. Setting this to false will hide all errors. This should be used in conjunction with WP_DEBUG_LOG so that errors can be reviewed later.
define( 'WP_DEBUG_DISPLAY', false );
The WP_DEBUG option was added in WordPress Version 2.3.1.
Starting with WordPress version 2.3.2, database errors are printed only if WP_DEBUG is set to true. In earlier versions, database errors were always printed. (Database errors are handled by the wpdb class and are not affected by PHP's error settings.)
Starting with WordPress version 2.5, setting WP_DEBUG to true also raises the error reporting level to E_ALL and activates warnings when deprecated functions or files are used; otherwise, WordPress sets the error reporting level to E_ALL ^ E_NOTICE ^ E_USER_NOTICE.