Answer:
This short play takes advantage of situational irony to build humor. A "still alarm" is defined as "a fire alarm given by telephone or by any means other than the regular signal device." This type of alarm is usually used in a firehouse to let the fire fighters know what type of fire they will be responding to.
The Still Alarm is set in a hotel room. The irony, and the humor, is that the characters don't panic. In fact, they act like perfect gentlemen. The director's notes even advise:
It is important that the entire play should be acted calmly and politely, in the manner of an English drawing-room comedy. No actor ever raises his voice; every line must be read as though it were an invitation to a cup of tea. If this direction is disregarded, the play has no point at all.
The bellhop keeps bringing news about the progress of the fire, but the other characters treat it as if it is no big deal. When the fire fighters arrive, one of them sees a violin in the room and starts to play it. So while the building is burning down around them, he plays "Keep the Home Fires Burning."
