SPDIF is a digital format that allows certain audio signals pass. Those are PCM 2 channel, Dolby Digital (up to 6.1 EX), and DTS (up to 6.1 DTS-ES). Those are the limitations of the SPDIF format which use Coaxial or Optical connections for termination between a source and processor (receiver, preamp, pre/pro).
When DVD-Audio and SACD came out they made no provisions for the format of connection for copyright protection purposes. DVD-Audio uses MLP Lossless which is typically 5.1 LPCM. SACD uses DSD (Sony's proprietary audio format) up to 5.1 of what I understand to be lossless sound. Since they didn't want to use SPDIF (coax or optical) they had to output the sound via Firewire as the digital connection. Most budget DVD-Audio and SACD players did not have Firewire, so the decoding for DVD-Audio and SACD had to occur inside the player and output over a usable 6 channel (5.1) analog output.
Think of it this way. When data is read from a CD it is purely digital (0's and 1's) and must be processed (converted) into a usable analog output. The player converts the digital signal via DAC (digital to analog converter) and the signal is now analog. If you wanted you could use a CD player's digital output (SPDIF; Coaxial or Optical) and the DACs in the receiver or external processor would be used instead of the CD player's. So the digital signal leaves the CD player and is processed into analog outside of the CD player.
Dolby Digital and DTS are different from PCM in that they are packed files. This means they are compressed to fit on the storage medium (DVD or some other medium), much like a .rar file. Just like a .rar file the bitstream must be uncompressed into usable data. So when it is uncompressed it would theoretically take up more space, but it is being read and processed only in one place (such as in a capable DVD player or receiver). Once the bitstream has been unpacked it is PCM and DACs convert the 5.1 signal to analog.
Lets say you watch a DVD on a DVD player with 5.1 analog outputs as well as SPDIF output/s. If you use the analog outputs the DVD player is decoding the 5.1 Dolby Digital signal and sending it out analog to the receiver. If you use the SPDIF (coaxial or optical) the signal is sent out from the DVD player in its digital form and is decoded inside the receiver or processor. The advantage to having the receiver handle the processing is that most receivers can apply post processing methods, such as bass management (cross over for the subwoofer and speakers). Most receivers can't apply post processing to 6 channel inputs because it requires that the analog input be digitized to apply them.
Now the new surround formats like Dolby TrueHD, DTS-HD, and Dolby Digital Plus can be output via HDMI (this is assuming full HDMI 1.3 compliance on both ends meaning the HD player and the receiver/processor). Dolby TrueHD, DTS-HD, Dolby Digital Plus, Dolby Digital, and DTS are all bitstream packed audio files that must be decoded (converted) into PCM and after which the DACs convert the PCM into analog. That would have all occurred in the receiver in that scenario.
There are two other ways to get similar performance. The next best way, and arguably no better than the first, is to have an HD player decode the bitstream Dolby TrueHD, DTS-HD, or Dolby Digital Plus inside the player at which point the signal has become multichannel PCM (LPCM specifically, "L" stands for Linear). This LPCM signal (which currently can reach up to 7.1) can be sent out of the player via HDMI to the receiver which can use its DACs to convert the signal to analog and also do any post processing that is necessary.
The last way to handle the Dolby Digital Plus, Dolby TrueHD, and DTS-HD formats is to have all processing and conversion occur inside the HD player and be output via analog outputs. As mentioned before most receivers don't allow post processing to occur via multichannel analog inputs. If the HD player has its own bass management it may help if you have no other means.
(note: For the multichannel LPCM to work you must have a receiver or processor with at least HDMI 1.1 (repeater) to get a minimum of 5.1 LPCM from the lossless HD audio formats.)
Sorry for the long post and I can only hope this explains everything.
