Do you recognize this logo on the left? You may see it on the back cover of some of your CDs. This means your CD has High Definition Compatible Digital (or HDCD) information encoded in the disc. HDCD is an encode-decode process that improves the sound quality of HDCD-encoded CDs. If you play the HDCD disc in a CD player that includes the HDCD decoder, the audio is played back at 20-bit 44.1kHz. These CDs are also backward compatible with a regular CD that uses the standard Redbook CD specification (which is any CD that will play in a CD player). So when you play an HDCD disc in a regular CD player, it plays just like any other CD at 16-bit 44.1kHz.
I'm not sure exactly why these discs sound better. According to the wikipedia article for HDCD, it could be due to the mastering engineers taking advantage of 4 more bits of dynamic range and digital interpolation filtering which results in a more natural, open, and accurate sound reproduction. I think the engineers that take advantage of HDCD are probably more careful when mastering, use less compression, and are concerned about overall sound quality, just like they are when mastering for vinyl, SACD or DVD-Audio.
The only way to take advantage of HDCD with a PC was to play the physical disc with Windows Media Player. Microsoft actually bought the developer of HDCD technology, Pacific Microsonics, and all their intellectual property, in 2000. If you ripped your HDCD disc to your computer's hard drive (or media server), the audio would not play back at the higher resolution. It would just play back as a regular 16-bit 44.1kHz CD.
I recently discovered that you could use a combination of tools to convert HDCD encoded audio files into a higher resolution and take advantage of the higher quality recordings. It's important that your ripped CDs are exactly the same as the original CD. If they are compressed using a lossy format like MP3, this will not work. If you use lossless compression like FLAC or lossless WMA, it should work. One method is to use the custom little decoder program 'hdcd.exe'. This little tool will input the 16-bit WAV data and if it finds the embedded HDCD info, it will upconvert it to 24-bits. The last 4 bits of this 24-bit file are empty, so your DAC just sees it as a 20-bit file. For more information on how to use this command line utility read this thread at Doom9's forum. Apparently it will still work with non-HDCD encoded files, but the volume will be cut in half. So maybe this isn't the best method. Or, supposedly there's a way to check if the file is HDCD encoded using hdcd.exe in test mode. So it's probably a good idea to check if the file is HDCD encoded first.
Another method, which I believe is a lot more convenient, is to use dBpoweramp. Using dBpoweramp's conversion utility, you can activate their HDCD plugin, which automatically detects HDCD encoded files and decodes to 24-bit. If the file is from a non-HDCD audio CD, it is left as 16-bit. Again, it will only work if the file is exactly the same as the original HDCD encoded CD. So it had to have been ripped to uncompressed WAV or losslessly compressed FLAC, lossless WMA, etc., etc. When you convert the file just use the same encoding method (I usually just use FLAC) and overwrite the original file.
You can now play your decoded 24-bit 44.1kHz audio file on your PC with any software player. Now, all you have to do is dig through you CD collection and check the back of the disc for the HDCD logo and go to work. If these CDs have already been ripped, then use the dBpoweramp converter to decode them to the higher resolution. Some HDCD encoded discs do not have the logo printed on their back cover, but still include this capability. You could always use dBpoweramp to test if they have HDCD, but that might take a lot of time. You can also search the web for a list of HDCD encoded CDs. I was able to find this list on Head-Fi's forum. So before you dig through all your CDs, you might want to check to see what's on the list. I plan to convert all my HDCD encoded CDs to 24-bit when I get the chance.