A long time ago, the entire telephone network was analog. This was bad, because as a voice went farther down the line, and through more switches, the quality became worse and worse as noise crept in. And there was no way to eliminate the noise, no way to know what the signal was supposed to be. Digital encoding promised a way to encode the audio such that you'd know what the signal was supposed to be. As noise crept in, you could eliminate it throught the phone network, assuming it wasn't worse than the variation between different digital encoding levels.
With the transistor revolution, this theory became possible, and the phone companies began converting their own networks over to digital. Today, you have to search pretty hard to find a phone company switch that isn't digital. They call their network the Integrated Digital Network, or IDN.
This solved many of the phone company's problems. However for a variety of reasons, it has been attractive to make the phone network completely digital, from end to end. For computer users, this is ideal, because we can eliminate those clumsy modems, and will hopefully benefit from higher speed. For the phone companies, they can eliminate the last of the noise and loss from the audio data. And for dreamers, this will enable a wide variety of different services to be delivered to the customer over a single interface.
ISDN was originally envisioned as a very fast service, but this was a long time ago when it was hoped to have fiber all the way to your house. It turned out that running all that fiber would be too expensive, so they designed ISDN to run on the copper wiring that you already have. Unfortunately, that slowed things down considerably - too slow for quality video, for instance.
ISDN has been very slow in coming. The standards organizations have taken their time in coming up with the standards. In fact, many people consider them to be out of date already. But on the other side of the coin, the phone companies (especially in the U.S.) have been very slow at designing products and services, or marketing them with ISDN in mind.
Things are starting to pick up, but still very slowly. ISDN is available now in many places, but it is not widely used. Further most of the products and services that people have forecast for ISDN still aren't available. For this reason many people say that ISDN also stands for "It Still Does Nothing".
There are two parts of a telephone network: the phone company's part, and the customer's part. The customer's part today is largely just the telephone, some house wiring, and some connectors. The phone company's part is lots more wire, fiber, switches, computers, and lots of expensive and complicated stuff.
ISDN is concerned (almost) entirely with the customer's part of the network. ISDN gets the data from you, to the phone company in a standard way. What they do with it in order to get it to its destination is entirely up to them. This is a very simple, important concept. If you understand this, then when someone says something like "SONET is the future of the modern telephone network" you'll know that they're talking (mostly) about what goes on inside the phone company, and between phone companies. They are probably right, but it is also true that "ISDN is the future of the modern telephone network" especially if you mean B-ISDN. They're just the future of different parts of the telephone network.