Direct-Stream Digital (DSD) is the trademark name used by Sony and Philips for their system of recreating audible signals that uses pulse-density modulation encoding.
SACD audio is stored in a format called Direct Stream Digital (DSD), which differs from the conventional PCM used by the compact disc or conventional computer audio systems.
DSD is 1-bit, has a sampling rate of 2.8224 MHz, and makes use of noise shaping quantization techniques in order to push 1-bit quantization noise up to inaudible ultrasonic frequencies. This gives the format a greater dynamic range and wider frequency response than the CD. The SACD format is capable of delivering a dynamic range of 120 dB from 20 Hz to 20 kHz and an extended frequency response up to 100 kHz, although most currently available players list an upper limit of 80–90 kHz and 20 kHz is the upper limit of human hearing.
Source: Wikipedia
The obvious benefit is the wide frequency range allowing you to record without a filter.
If one record using PCM, the input signal should be band limited (low pass filter).
Record e.g. at 48 kHz then the Nyquist is theoretically 24. Any signal > 24 in the input will not be captured properly and hence generates an erroneous value.
The downside is that the noise shaping generates a strong amount of high frequency noise.
This is one of the DSD paradoxes, the bandwidth is tremendous but above 20 kHz the music signal will start to be drowning in the noise.

Accuphase DP-85, 1/3-octave spectrum of dithered 1kHz tone at -150dBFS, with noise and spuriae (from top to bottom): DSD data, 24-bit PCM data (right channel dashed).
Source: Stereophile

DSD quantisation noise with a sampling rate of 64 times 44.06 kHz.
Malcolm Hawksford, Essex University, UK
Source: HDTracks
To play SACD a low pass filter is recommended.
All these strong high frequency content might fry your tweeters!
There are two good reasons to convert DSD to PCM
Again, when converting you need a low pass filter.
Bruce Brown converted DSD to PCM using Weiss Saracon software.
Much to his surprise the conversion to 88.2 and 176.4 yielded the same frequency content.
Obvious the (needed) filter applied by Saracon doesn’t allow for anything > 40 kHz.
An 88.2 kHz transfer will need a brickwall filter by 40 or 44 kHz, so most of the noise is filtered out anyway. A 176.4 transfer has more flexibility. They have to decide how much noise they want to let through, but they have the advantage of not requiring such a sharp filter. This results in better sound quality.
Source: Charles Hansen
Normally you need a dedicated player for DSD. Your PC won't play it without converting it to PCM first. A couple of guys formulated an open standard allowing direct playback on a PC. Not only must your hardware (DAC) support it but your media player as well. At the moment JRiver Media Center in combination with Playback Design DAC works. As XMOS supports this standard and their USB receiver is used in many async USB DACs, probably more DACs will support this standard in the near future.
The bit rate of DSD (2.8224Mbits/sec) looks impressive but it is less than a 24 / 176 PCM. The trick is to pack the DSD in a PCM stream and put a marker in this stream allowing the DAC to discriminate between PCM and DSD.

DACs supporting DSD over USB can be found here.
DSD has a sample rate of 2822.4 kHz.
This is 64 times the rate of CD (44.1 kHz).
This is the standard.
Korg studio recorders allow for even higher rates (5.6 MHz).
The Korg AudioGate software allows for upsampling to 11.3 MHz or 256 times the Redbook sample rate.
Due to these differences in sample rate, you will find references as DSD64, DSD128 and DSD256.
The DSD catalogue is very limited at the present.
Source: Michael Lavorgna
176/24 PCM and DSD64 are about the same resolution, they just have different distortions. Thus it seems a matter of preference which one is "better". However, converting between them is not such a great idea as the mismatch retains the worst aspects of PCM (smeared transients from the filters) and DSD64 (high frequency noise that starts at 25 kHz). DSD128 does not seem to have the problem with high frequency noise that DSD64 has, so this tradeoff seems moot, at least on my system.