Here's a conversation I have had several times with numerous different students:
Student: Master Daniel?
Me: Mister Daniel, I'm not master yet. Although...that has a nice ring to it.
I would argue that just because someone calls you a master, doesn't make you a master. Otherwise I'd be a master already, and I'm definitely not there yet. If we're generalizing it, master can be used in a couple of different ways:
1. Someone who is recognized as the top in their category, either by an official association or by victory in a competition. For example, a chess master or grandmaster is ranked by the organization based on their skill relative to other players, or a Master Chef is someone who was won a master chef competition.
2. Someone who is an expert in everything of their trade. For example, let's say you take your car into the shop. One mechanic knows how to do basic repairs, but has to google everything else. Another mechanic will ask for help if he doesn't know something. The master will know 90% of the questions that the others have to google, and for the other 10% he knows the information he needs and exactly which reference book to get it from. He has confidence in his craft, and you can be sure that if you ask him a question, you'll have the correct answer in minutes. Whereas the other guys may take ten minutes to figure out what you're asking, the master mechanic will hear you say "it's making a kind of clunk-ting-clunk" and will stop you there, and say "give me 5 minutes and some duct tape" and your car is fixed.
3. Someone who is considered a leader in their field. This is someone that others would seek to apprentice under, learn from, or would go to for advice. By "others" I mean people beginning in the field or even those who are already proficient. For example, I already have several years experience in IT and a few years at my current position, so I am quite proficient at what I do. However, there are others in my department I go to for advice, because I consider them to have a mastery of the field.
4. A rank, such as in Taekwondo how 4th or 5th Dan can be considered Master and 7th or up can be Grand Master.
Any of these can apply to martial arts, although I would argue that 2, 3, and 4 are generally the ones you would consider. Hopefully someone would have all 3: the complete understanding of the art, the leadership skills required to properly teach the art, and the rank and approval of the organization (if applicable). For example, my Master has in various organizations/arts: 6th Dan and 5th Dan in different TKD organizations, 4th Dan in Hapkido, and 2nd Dan in both Special Forces and in sword. It is clear when he performs his techniques that he knows his stuff and has built up the muscle memory from decades of training, and he does a great job not only teaching the classes, but in training me to teach as well.