Would often make Bach play introductions only, to demonstrate organ (4)
I believe the answer is:
womb
'organ' is the definition.
(womb is a kind of organ)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for womb that I've seen before include "Place of gestation" , "Organ housing fetus" , "Organ in which young develop" , "Generative organ" , "Embryo's home" .)