OK, may be more than you want to know, but here goes.
To represent music in a digital format, you take the analog wave form (see the picture in the PCM link to Wikipedia) and sample it at enough points to faithfully represent the music. If you take too full samples you do not faithfully represent the music. If you take too many samples you can faithfully reproduce the music but you use a lot of extra disk space and the processing of the data can become difficult, even for a powerful computer.
There is a theorem in information theory (Shannon - Nyquist Theorem) that says if you sample at twice the highest frequency in an analog signal, you can exactly reproduce the sounds up to that frequency. Since the limit of human hearing is often set at 20 KHz, then taking samples of the waveform at 40 KHz will reproduce everything below 20 KHz. The CD sample rate was originally set at 44.1 KHz because there were electronic parts available that worked at 44.1 KHz and that would reproduce music up to 20 KHz. That means taking 44,100 samples every second, which is a lot of data.
Each sample represents the height of the waveform. For CDs each sample was measured using 16 bits, which gives a number between −32,768 through 32,767. That gives a very accurate value for the waveform at each sample point.
One problem with sampling at 44.1 KHz, is that when you turn it back into analog, you get lots of "noise" above 22 KHz. The noise was not present in the original waveform, so you want to filter it out. Unfortunately, the filter that does that can introduce noise below 20 KHz, which means that the process has not done a exact job of reproducing the original waveform.
One way to overcome the 22 KHz filter problems is to sample at a higher rate, like 88.2 KHz or 96 KHz or 192 KHz. This was the reasoning behind hi-rez audio, which was introduced commercially in 2000 as DVD- Audio or DVD-A. Both CDs and DVD-A use PCM for the data.
An alternate hi-rez format (SACD) was develop at about the same time by Sony and Philips. It used a much higher sample rate (2.8 KHz) but only 1 bit of data - up or down. This is the DSD format. 2.8KHz is 64 times 44.1 KHz so this form is sometimes called DSD64. In terms of data, there is 4 times the amount of data as a CD (64/16), so it should be able to reproduce the original waveform more accurately than a CD can. It is comparable to the amount of data in a DVD-A.
There are some issues with DSD. Because the data is only 0 or 1, there is high frequency noise produced when the data is turned back into analog. So, Sony and Philips put in filters at 50 KHz to remove that noise.
But, the bigger problem is that it is very hard to manipulate DSD data. It takes a huge amount of compute power to make changes to the DSD data, so the traditional editing that a sound engineer does is basically impossible to do. So, the editing is actually done by converting to PCM and then converting that back to DSD. Some producers are now doing their editing only in the analog mode, so that there is no PCM involved but that is a laborious process.
The engineers at Sony and Philips thought the DSD format sounded better than hi-rez PCM, so they used it for their SACDs.
PCM has remained the dominate format since it is easy to generate, easy to edit and easy to transmit. Some diehards hold on to DSD since they think it sounds better. After an initial flurry of activity a few years ago, DSD has still remained a very secondary format used only by a small part of the high end market. But some people swear by it.
The Wikipedia articles have more detail, but that is an overview.
