I've been studying this problem for quite a while now. Frankly, most of these answers are clearly wrong, and misunderstand the issue.
This problem has nothing to do with your iOS version, restore, settings, username, or password being incorrect unless you were never able to send email at all. I have experienced it on 4,5s, and iPhone 6, with many different iOS versions and it is never fixed by an upgrade.
Basically, If you were sending email ok an hour ago, and it's suddenly stopped working, there is no need to change any settings.
This problem has something to do with switching cell towers, routers, locations, protocol paths, etc. if I drive across town, fly on a plane, etc. I often notice email will no longer send until I do a two finger reset. Sometimes switching to wifi, or switching off wifi if you've been using it and moving the email sends to the lte cellular network , will fix it as well.
Photos or other attachments will often be the emails that won't send, while short texts only will still work. It seems once there has been a failure to send one, no others will go through indicating the router or cell tower is remembering the failure, and refusing to try again. Poor signal, or switching towers while in the middle of sending may cause it as well.
If the two finger reset, isn't working, try turning off wifi to force using the cell network will work. Other times the cell network may be getting too many errors on your large attachment and moving to a location with good wifi will work. Once it fails once, simply getting a better signal isn't enough unless you use one of these other methods to force it to forget the previous error an actually try again instead of just pretending to do so Seems to be required.
Sometimes resetting, and immediately trying again still won't work, while resetting and waiting a while before trying again, will. Again indicating the network is remembering the error.
Somebody who actually knows at a cellular company or Apple, please explain the technicalities. The rest of you are just spreading folklore, or coincidental fixes, imho.
