I'm typing in my Apple ID and password in correctly on my iPhone 6, but it's not working?

My phone turned off iMessage. I keep getting "Verification Failed" and that "there was an error connecting to the Apple ID server". I KNOW that I'm typing in my username and password correctly. I even was able to log onto Apple s website with it, but not my phone for some reason. Why is this? How can I fix?
iPhone 6, iOS 9 (not the newest iOS though)

Try restarting the phone -- hold down the Power button and Home button at the same time for about 6 seconds.