Stands for High Density Compatible Digital.
A patented process for recording and mastering audio CDs which somehow takes the 16 bit samples of audio information and effectively gives 20 bit resolution for the audio. It does this by dithering the audio signal in a way that does not affect performance on non-HDCD-enabled CD players, but provides increased dynamic range and clarity if the player supports HDCD.
HDCD is available on certain high-end CD and DVD players, and is sold by Pacific Microsonics to semiconductor manufacturers who sell DAC chips to manufacturers who put it in their products. HDCD based players have an indicator light that lights when a HDCD disc is played, but the company who makes the technology believes that the improved digital filtering will also improve the sound of non-HDCD-encoded CDs.
I only have a cheap CD player which does not support HDCD, so I can't tell you if it's actually better. I'm currently looking for a wealthy, audiophile friend who has an HDCD player that I can borrow for a few minutes and do an A/B comparison.
Oh, and if it sounds too good to be true, Pacific Microsonics was purchased by Microsoft in the fall of 2000.
(some material cribbed from the HDCD website, curiously at www.hdcd.com.)