Here`s wikipedia`s definition of 'master class'-
''A master class is a class given to students of a particular discipline by an expert of that disciplineusually music, but also painting, drama, or any of the arts.
and The difference between a normal class and a master class is typically the setup. In a master class, all the students (and often spectators) watch and listen as the master takes one student at a time. The student (typically intermediate or advanced, depending on the status of the master) usually performs a single piece which they have prepared, and the master will give them advice on how to play it, often including anecdotes about the composer, demonstrations of how to play certain passages, and admonitions of common technical errors. The student is then usually expected to play the piece again, in light of the master's comments, and the student may be asked to play a passage repeatedly to attain perfection. Master classes for musical instruments tend to focus on the finer details of attack, tone, phrasing, and overall shape, and the student is expected to have complete control of more basic elements such as rhythmpitch. The value of the master class setup is that all students can benefit from the master's comments on each piece.
Many concert performers have given master classes, including such greats as Franz Liszt, Yehudi Menuhin, Isaac Stern, and Vladimir Horowitz. Often, a touring performer will give a master class the day before, or the day of, their performance in a particular city. Giving a master class before a concert provides both artistic stimulation for the performer and a means of obtaining a larger audience.
Aspiring classical musicians, and their teachers, typically consider master classes to be one of the most effective means of musical development, along with competitions, examinations, and practice.
Some Musical Theatre composers will also give master classes to college students studying performance.''
I think most conductors go to university and study music, probably obtaining degrees. There would be conducting classes there. However, I`m fairly sure they probably have master classes with other, more established conductors. Or at least study under other conductors' tutelage. Not sure, having never studied conducting...