Why does it say my email was “rejected by the server because it does not allow relaying” when I try to send it?

If you try to send an email from your iPhone on iOS 8, or an earlier iOS for that matter, and get an error message that says “A copy has been placed in your outbox. The recipient was rejected by the server because it does not allow relaying,” chances are you need to check your outgoing mail server settings. Here’s how: