Nice posts again, guys! Vandermeulen, you make my main point much more simply than I did - everyone must decide for themselves through experience what they want their system to sound like.
However, I must repeat that there is no such thing as absolute neutrality. Any piece of audio equipment is going to contribute some "coloration." By way of explanation, let me go back to the recording studio example. These are almost always rooms that are almost completely dead. This is not because the engineer is trying to emulate some sort of absolute neutrality, as someone suggested. In fact, it is for the completely opposite reason - so the engineer can play with the recording and make it sound exactly how he wants it to via instrument placement, miking, mixing, and almost always the addition of digital effects that do not actually exist in the music being recorded. In other words, the engineer is eliminating what he calls "room noise" as much as possible and putting his own "coloration" onto the recording. And every single engineer will have a completely different idea of what this ideal "coloration" is, just as every acoustician will have a different idea of what an ideal concert hall should sound like.
Same thing with designers of audio equipment. They all have a very specific idea of the sound they are looking for when they start out, otherwise what the heck is the point?! They are trying to create something that sounds like their ideal, and every one of them will have a slightly different conception of it. This is what creates "system-induced coloration," as someone put it.
So in the end, Cbw723 is correct, I think - it doesn't really matter exactly how one defines these terms, as everyone is going to have a slightly different conception of them, and their own set of preferences. One can only decide what one's own ideal is for a piece of equipment (and how it matches up with other pieces of equipment in the system, of course) by experience. Someone who listens to almost entirely electronically-produced music is almost certainly going to have a very different opinion about all types of equipment to someone who listens almost exclusively to acoustic instruments, for instance. As for the question "is there a way to know if I'm hearing the music better, or just my system," I reply that again there are no absolutes here. Even assuming you are referencing live music (which not all audiophiles do - some of them, for various reasons, do not want their systems to sound anything like live music), there are many different types of venues and sounds, so your ideal may be very different from mine. That's another reason why there are so many different types of audio equipment out there - there are many different tastes, and no one of them is inherently right or wrong. It depends on what your sonic priorities are, and only you can determine that, through experience listening to different types of equipment and systems, always referencing this to your ideal of what live music should sound like, realizing that your system can never really recreate this.
Speaking of trying to recreate the live event, I should add, Byron, that no, I don't agree that the "least amount of coloration" will result in the closest thing to live music, necessarily - in fact, many (though of course not all) systems I have heard described as neutral actually sounded lifeless, without any sense of space, color, ambience, etc. - nothing like live music. My point is that just as all live music is "colored", so is all reproduced music - one must choose the type of "coloration" one wants in one's system. If any ten audiophiles assemble a system that they consider very close to whatever their conception of "neutrality" is, I guarantee you will have ten completely different sounding systems.