Hello, Liz55Go
Thank you for visiting Apple Support Communities.
There could be a couple causes for this and I will include a couple solutions. Sometimes the account credentials need to be authenticated and can cause this message. Try closing all applications in multitasking and power cycle the device. Two step verification may be enabled causing this error, try checking if this feature is enabled by logging into the mail client via a web browser on a computer, disable and test. If this issue is with a Gmail account then see the second article below. The last solutions I could recommend would be in the last article below.
iOS: Force an app to close
http://support.apple.com/kb/ht5137
iOS: Gmail account will not connect to Gmail server
http://support.apple.com/kb/TS3058
iOS: Troubleshooting Mail
http://support.apple.com/kb/ts3899
Cheers,
Jason H.