A good artist can make an amazing likeness of a person's face with canvas and paints. But if all they have to work with is bark and a charred stick, it won't look that real. In technospeak, if the signal to noise ratio becomes too low, the data will not be transmitted properly. When information is transmitted digitally, it is translated into ones and zeroes, transmitted, then translated back. This process can be repeated infinite times, and as long as the method of translation is the same, the data will not lose quality.
Digital transmission can also use a lower quality medium and remain true.
Whether using paint and canvas or bark and charcoal the ones and zeroes still look like ones and zeroes. Clearly, now that we have the technology to encode our communications digitally, it is most efficient to transmit them digitally too. Constant fast paced innovation has made high tech companies masters of rolling out new products, and the 56k frenzy is no exception. In creating a new 56k standard, modem companies have the chance to sell new modems to both the end users and the ISPs, so it served their purposes to exaggerate the benefits of the 56k technology. Most ISPs have digital connections to the phone company's main switches.