But based solely on what you posted, the problem is the following:
define( 'SMTP_USER', '[email protected]' ); // The email address I use when I log in to the wp-admin page
define( 'SMTP_PASS', '123password' ); // The password I use when I log in to the wp-admin page
define( 'SMTP_HOST', 'localhost' ); // I am testing this on localhost
define( 'SMTP_FROM', '[email protected]' ); // Also the email address I use for logging in on the wp-admin page
The script you posted is to define the connection information to an SMTP server. Unless you are actually running an SMTP server on your localhost with the login credentials you supplied in the other constant definitions, then that is why your script is failing.
The SMTP_HOST constant must define the location of the SMTP email server you are trying to connect to (such as
Likewise, the login information should not be what you use to login to WordPress. You indicated in your comments that these are the login credentials that you use logging in to wp-admin. But what they should be is the login credentials for the email account on the SMTP server you are connecting to.
If you have an email account you are intend to send through, check with your email provider. They should be able to supply you with the correct connection information.