in which a master
gives detailed instruction, with examples, to one or a small number of pupils, while watched by a larger number. It is particularly used in reference to musician
These days master classes are often done before large audiences at festivals, or put on television (well, "often"... I suppose it depends what sort of television stations you have round your neck of the woods), and are surprisingly enthralling, despite how hesitant and fragmentary they are, with the pupils playing only short snatches and those over and over, and the master seldom doing any virtuoso work.
In a recording, or on stage, you never hear how musicians speak, or think about their work, unless you get a brief bit of rehearsal; a master class is an opportunity to learn a different side of the master.
Terrence McNally wrote a play Master Class about Maria Callas teaching at the Juilliard School.