What is a discussion play? How can it be proved that "Arms and the Man" is a discussion play?
A discussion play is a play in which the play focuses on discussing specific ideas--it focuses on them, at times to the exclusion of fully characterizing the characters or making the action dramatic. It is linked to the closet drama (meant to be read, not performed) and the problem play (focusing on the problem dramatized).
You'd determine if Shaw's play falls into this category by looking at the amount of time spent discussing ideas in the play, and how that discussion relates to the action.