DSD is one of an many possible variations of Pulse Density Modulation, which can be one or multi bit, and two or multi levels. DSD, a marketing term coined by Sony, is 1-bit two level PDM (Pulse DENSITY Modulation). It is the result of the modulation of a free running bit clock (2.82MHz, 5.6MHz etc.) by an analog signal yielding a bit stream whose bit density is relatively proportional to the signal level. Like a picket fence in time with a greater or less density of pickets describing the relative signal level.
One of the characteristics of a PDM (DSD) bit stream is there is no numerical level represented, just a relative level difference contained in the bit density. In other words, it's a digitally store-able and retrievable analog system. It's also the reason the bit stream can not be arithmetically processed in a digital computer, and must be converted to a absolute digital value based system, like PCM, to be processed. There's no arithmetic value represented, unlike PCM.
PCM (Pulse CODED Modulation) is an example of a absolute value digital based system (like the stand alone individual frames in a motion picture, each frame is a value), which can readily be processed in a computer. The fly in the ointment is every time a format conversion takes place, some signal/sound quality is lost. The problem is recordings typically require post processing in the mastering stage, and unfortunately the conversion of PDM (DSD) to PCM inflicts losses that are easily perceivable. Particularly in acoustic music in spaciousness cues.
What 'DSD naysayers' (for lack of a better term) do not point out is that ALL analog to digital converters available today, and for more than the last ten+ years are PDM front ended. That's to say, all recordings and transcriptions produced today start out as a high clock rate DSD like bit stream, and must be converted to PCM for mixing and computer effects processing. Even 96KHz PCM, which is a quarter of the PCM sampling rate used to master many acoustic music recordings, originated as a DSD like bit stream.
As a side note, don't forget that recordings that are analog session mixed before any conversion, and any Sony Sonoma or SADiE Digital Audio Workstation (DAW) produced recordings not using any PCM interstage conversions. Granted, these practices and systems are not used in pop music recording, but they are a significant percentage in the acoustic music production world.