iPhone: Phone handset icon?

I have an icon I've never seen before right next to the battery icon on my iPhone all of the sudden. It looks like a phone handset avove a keyboard (the keyboard is 7 dots). Also, all of the sudden, I'm being asked to enter a voicemail password when I tap on anything. I can't seem to turn that off, although I never turned it on. Does the icon have anything to do with that?

Thanks for all help in advance!