The unmodulated carrier is simply the electricity your phone operates on, the steady and continuous current your telephone company provides. It carries the conversation. When you talk the phone impresses your conversation on that current. Conversation causes the current's resistance to go up and down, that is, your voice varies or modulates the carrier. Below is a simplified view of a digital signal.
Current goes on and off.
No wave thing. You might wonder why you can't go digital from your computer to the local switch. Well, that's exactly what expensive services like T-1 provide. But with T-1 you need two pairs of twisted pair, costly equipment at each end of the line, and the telephone company to condition or prepare your twisted pairs for fully digital service. They also need to change the voltage on your line from about 52 volts to about 135.