(This text was written specificaly for D&D, and may thus need alterations.)
Neutral characters do whatever seems to be a 'good idea'. They don't feel strongly one way or the other when it comes to good vs. evil or order vs. chaos. Most neutral characters exhibit a lack of conviction, or bias rather than a commitment to true neutrality. Such characters think of good as being better than evil (after all, they would rather have good neighbours and kind kings than evil ones), but are not personally committed to upholding good in any way.
Some neutral characters commit themselves to a philosophy of neutrality. These people are extremely rare in a world where most people make value judgements, and are said to be "true neutral."
True Neutral characters see good, evil, law and chaos as simply prejudices and dangerous extremes. They advocate that the middle way of neutrality is the best and most balanced road in the long run.
Some true neutral characters will actively support neutrality and balance in the world. They will avoid having to support any one side, whether that be good or evil, order or chaos; and will work to see that all of these forces remain in balance.
Other true neutrals are simply characters who are tired of this concept of 'morality', and find that they draw no meaning from it. These characters are not neutral out of choice, but simply that they care not either way - they are passively neutral, but still falls under the banner of true neutral.