The stock ticker was the direct result of the most-recent technology of the day - the telegraph machine. Thomas Edison invented the first ticker machine in 1870 and the technology raced at a speed of about one character per second. George Scott invented the first self-wind ticker machine, though many of the machines were actually manufactured in Thomas Edison's factory.
Consider the early technology in very simplistic terms. At one location, there was a special writer. At another was a receiver - the ticker machine itself. The two were connected by a wire similar to telegraph wire. The writer and receiver communicated via analog signals. The receiver printed out a continuous string of information on a long piece of paper, known as the "ticker." These long strips of paper were often cut into pieces to form confetti, and thrown from windows during parades. As you can see, the technology - at the top of the field at the time - has since become hopelessly outdated.