Okay, I solved my own problem with the help of a thread on another site. I am posting my findings here in the hope it may help someone else.
1. Go to Settings
2. Select "Mail, Contacts, Calendars"
3. Select the email account with the problem (being rejected by the server...does not allow relaying)
4. Scroll down to "Outgoing Mail Server"
5. Select SMTP (mine says "SMTP outgoing.verizon.net", because my email account is with verizon)
6. Under "Primary Server" select the server (again mine says "outgoing.verizon.net")
7. Make sure Server is ON
8. Make sure the User Name and Password are filled in (mine was Not filled in)
9. Click "Done" in the upper right corner of the screen
10. Now go back to the email account screen
11. Click "Done" in the upper right corner of the screen
That's it, it worked for me and my email went out right away.
I have this problem, but the solution described above (and seen on other sites) isn't resolving it. Any other tips?
Check the SMTP settings for your email provider (contact your email provider), and follow the steps provided on previous posting replacing SMTP settings information with the settings provided by your email provider.