I've had that pop up on my S4 before too. I did a restart, input my credentials and it was gone. Looks like an S4 specific glitch. What carrier you with?
I had this problem with my Yahoo mail account.
If this is the case, just download the Yahoo mail app and remove your yahoo account from the stock email app.
Change Incoming IMAP Server address from "imap.mail.yahoo.com" to "android.imap.mail.yahoo.com"
Change Outgoing SMTP Server address from "smtp.mail.yahoo.com" to "android.smtp.mail.yahoo.com"