HDCD is a coding system developed my Pacific Microsonics ( and later bought by Microsoft). It purports to perceptually "squeeze" more info into 16 bits, but it truly is still 16 bits. It's not a new format, per se, like DTS is, and it's strictly 2 CH. To realize the "benefits" of HDCD you need a player that can decode it. But an HDCD-encoded disc will play back very nicely on any regular CD player.
FWIW, some while some claim they sound better, others claim that non-HDCD encoded discs will sound audibly worse on an HDCD-equipped deck. Supposedly it adds distortions to the sound, and possibly noise. Myself, I can't say I can percieve any improvements from HDCD, but then it's usually not possible to A/B the same material encoded vs standard.
My advice in summary: don't sweat HDCD. Any improvements are likely to be extremely subtle at best, but it doesn't do any harm to play them on a regular player.