SMTP error codes are generally broken down into two categories of messages.
The first is 4xx smtp error codes. Any error code in the 400's is a temporary error. You can infer from this that your outgoing mail server will continue to try and send the email in the hopes that it can be delivered at a later time.
The second is 5xx smtp error codes. Error codes in the 500's are permanent errors. When a 5xx error is encountered your outgoing mail server should immediately stop trying to send the email and send you a bounce message, usually from mailer-daemon, letting you know that the email could not be delivered.
Both categories of error codes should also provide a specific reason for why the error occurred allowing you to troubleshoot the problem and take the appropriate action going forward.