In your own words, what makes a Master woodworker, Master knife maker, Master box maker, or Master craftsman?
Lot of good responses above, however everyone seems to left out...
Attention to Detail - A true master at any craft will pay great attention to detail. Even the tiniest of details. This will of course, over time become second nature in all he does, and he may well not even think about it while doing so.
Beyond that, and having been touched on above...
Being a Visionary - The ability to see projects in one's mind, know where you want it to go, before planning.
Adaptability - Being able to adjust when things don't go as planned.
Experience / Knowledge / Practice of Craft - Adaptability and at least to some extent being a visionary, is typically gained through experience and practice of the craft. The knowledge gained in said practice is instrumental in aspects above. While attention to detail can be and often is a personal trait, the experience to see every little detail is instrumental in fulfilling that aspect of one's personality.
What advice would you give to the novice or amateur woodworker aspiring towards such an achievement?
No one, since the beginning of time, has ever been born a true master at his craft. One may be born with all the ability in the world, they may be visionary, they may pay attention to detail, they may be knowledgeable of a craft, but without a great deal of practice of that craft, no one has ever attained master status.
Practice, ask questions, learn from your mistakes, repeat... A true master never stops learning.