The word has lost any relationship to its Latin root - magister, which meant teacher. It's lost it in other languages too - a magistrate is a special court in some countries, or a masters degree/study in others; master is, well, a master.
It has come into Serbian vie German Meister, which there and then meant "a master of his craft", i.e. a highly skilled worker who'd have apprentices. The apprentices called him Meister... so it came to mean a craftsman, a technician, or in today's language, a contractor.
Except there is, in 99% of the cases, no contract. Your majstor, most probably, has a day job somewhere, and if he's installing your AC, heating, or any major appliance that they sell on his job, he may appear in the uniform of the company, but he's working off the books. That way his employer pays him less (at least no overtime), pays less taxes etc, and this guy can charge whatever the market will bear. The boss won't mind as long as he keeps buying supplies in his shop.
Working off the books also means there's no advertising. You need to know someone who knows and will pass you the phone number. You need to know a lot - when to haggle, when not; what supplies will be consumed and are they bought at a good price or is he in a deal with some shop; at how many places has he promised he'll come this Thursday to do the work, etc etc.
In some cases, you're expected to make coffee for the team (if there's more of them, when doing masonry) and even lunch. Most of them, however, bring their own food or just send one of the guys to the nearest supermarket.
Some of them will leave the place as clean as they've found it or better; with some you're lucky if they don't do much damage to whatever they pass by.
As for procuring the parts, the perhaps shady deal between the majstor and the shop (who actually recommended him or vice versa) means that there's an open tab which works both ways. In old times, the majstor would send you to buy this or that; with this kind of deal he either picks the stuff in the morning or just phones in and they deliver. When he's finished, he returns the unused supplies and then the bill is made final and then you pay. It's a matter of trust - you may need to check the itemized list, which may be long and contain terms unfamiliar to you, or you can just pay up and be happy that you didn't have to visit the shop ten times and be left with half a crate of unused paid parts.
The majstori who are fixing appliances are almost the most unpredictable - sometimes they'll openly say it's just a cold contact they found in 20 and fixed in 5 minutes and will charge you some pittance (but you better carry the thing to their shop); some will require that you buy parts (and then will keep the old ones to see if they can be fixed - like washer machine motors, which can be transformed into lawn mowers etc) even when they are not broken.
Fixing your car is a matter of sheer luck. You can end up having it fixed squarely and neatly in an hour, or it may take days until the parts are procured, then something else will break and you may just end up paying the mechanic what you paid for the car.