So this happened to me after I upgraded my web server. This message is telling you Mail can't authenticate using the information you have provided to the app. If this happened suddenly, most likely there was a change in the mail server you are logging into and you have to correct the mail account settings on your device, but first you have to figure out what changed on the mail server you are using.
In my case, the old mail server would serve SSL and regular mail through the same subdomain - mail.domainname.com - using different ports. On the upgraded server, only regular mail was delivered through mail.domainname.com, and secure mail using another subdomain name on the server host (i.e. securemail.domainname.com).
The account that was throwing the error was on ssl, so my choice was to reconfigure the mail server to serve mail through the same subdomain - mail.domainname.com - on different ports, or change the outgoing/incoming mail server names on the iphone device to reflect the new setup (securemail.domainname.com). I tried changing the settings on the iphone device first, which worked.
Eventually, I configured the new mail server to my liking, but that's a benefit of managing your own mail server.