Quick answer: The WordPress critical error is a PHP fatal error, usually from a plugin, theme, or exhausted memory. Check the recovery-mode email WordPress sends for the exact cause, or enable debug logging to read it. Then deactivate the offending plugin or theme, or raise the memory limit, to restore the site.
WordPress emails the site admin address a message titled about a technical problem, often naming the exact plugin or theme and offering a recovery-mode link. If you received it, that link lets you log in and deactivate the culprit directly.
No email? Add this to wp-config.php to capture the error:
define('WP_DEBUG', true);
define('WP_DEBUG_LOG', true);
define('WP_DEBUG_DISPLAY', false);
Reload the site, then read wp-content/debug.log - it names the failing file. Set these back to false afterwards.
Deactivate the named plugin by renaming its folder in wp-content/plugins via FTP, switch to a default theme if the theme is at fault, or raise the memory limit if the log shows memory exhaustion.
Why did this happen after an update?
An updated plugin or theme may be incompatible with your PHP version or another plugin. Rolling it back or updating PHP often resolves it.
Can I prevent it?
Test updates on a staging site first, so a fatal error never reaches your live site.
On SoftSys managed WordPress hosting our team can read the logs and roll back a bad change, and staging is available to test updates safely.