This is a server error, caused by the local mail exchange from PHP mail(). The error comes back from the mail server and is not a fault in the WordPress Newsletter plugin, it is a fault on the server.

The error is usually due to PHP mail() and/or sendmail not configured correctly but it could also be caused on some servers by incorrect credentials such as the From address or even an email sending limit reached on the server for the day/week/month/etc.

If you see this error, please contact your hosting provider and tell them that you are trying to use the local mail exchange to send emails using PHP mail() and copy/paste the "Could not instantiate mail function" error to them.

They can then tell you what the issue is and help you resolve it.