Your PHP installation appears to be missing the MySQL extension which is required by WordPress.
This error is generated in wp-includes/load.php. Go to your WordPress directory and go look at that file and search for the line that has the error message.
Look at the “if” statement above it to see what MySQL extensions your version of WordPress is trying to use. If it’s checking for “mysqli” and other MySQL extensions, that’s a good thing, and you just have to make sure one of those supported extensions is installed.
If it’s only checking for the “mysql” extension, the problem is that extension has been deprecated and is no longer installed with new versions of PHP. You have to either upgrade your WordPress installation, or see if it is possible to install the “mysql” extension with your version of PHP.