Rev A (see Notes)
I haven't seen a good explanation of interpolation/oversampling for the uninitiated, so I scribbled the following one:
"Oversampling" in the D-to-A process of a CD player is essentially a matter of calculating extra samples to be inserted between samples from CDs to make it easier to filter out the sampling-related stuff at the output of the DAC, leaving just the audio signal. I don't understand how these calculations are performed - one look at a DSP text and I think you'll agree that this is best left to large groups of mathematical geniuses. Suffice it to say that these calculations can be performed more accurately with DSP chips than in the digital filter section of DAC chips, and that the greater accuracy sounds much better.
The resulting samples don't represent a waveform with higher frequencies (which is theoretically impossible anyways - additional frequencies would imply the creation of additional information out of nothing), but the same waveform with a higher sampling rate than is required for its bandwidth - i.e. "oversampled." Again, the purpose of oversampling is to create greater frequency-separation at the DAC output between the stuff to be kept and the stuff to be filtered out, so that analog filters with acceptable phase characteristics can be used for this purpose.
As good as CDs can sound, they're still not as good as high-resolution PCM, or DSD, which is the gold standard of digital audio. Part of this reason is that the data from a CD has 16-bit resolution, and the process of upsampling it to 24 bits assumes that the data from the CD has a resolution of 24 bits and just uses it as is. (What other choice is there?) So, this in itself introduces distortion. But, because so much of our favorite music is available on CD at best, we have to make the best of this flawed format, and this includes DSP-chip-based interpolation which uses minimum-phase filter-algorithms.
While performing research into whether a certain A/V receiver also makes use of DSP chips for interpolation, I realized that using external digital filters in conjunction with DAC chips is nothing new. However, the use of digital filters which have minimum-phase characteristics, which Robert Harley of the Absolute Sound called "nothing short of revolutionary," is new. It's not external filtering or minimum phase alone, but the combination, that has produced the dramatic improvements in CD playback over the last few years.
Rev A: Added last paragraph