The number of bits refers to how many shades each individual sub-pixel can produce (for an LCD). Note that CRTs do a full pixel, so an 8-bit LCD is the same as a 24-bit (and 32-bit) CRT.
8-bit is your "true color" i.e. 32-bit in Windows. It means each pixel can produce 16.7M colors. 6-bit can only produce 262k colors, but due to a technique called frame rate control, it can simulate 16.2M colors. Thus 16.2M color monitors are 6-bit.
People say 8-bit monitors have better color quality; I've never noticed the difference, but I'm not a discriminating consumer. What is true though is that 6-bit monitors are cheaper to produce (and hence cheaper to buy), and the response time for 6-bit monitors is supposed to be somewhat better than that of 8-bit monitors.