The server rejected one or more recipient addresses. The server response was: 503 This mail server requires authentication when attempting to send to a non-local e-mail address. Please check your mail client settings or contact your administrator to verify that the domain or address is defined for this server ..
Suppose the server's name is example.com It will allow you only to send email to email@example.com addresses. If you want to send email to @hotmail.com you need to have an account on the server, so you'll have to login with your email and password before being able to send. Is it your own server ? Then look in the manual, otherwise check your provider's support.