The phrase "pull out all the stops" comes from the world of music, specifically from musical terminology relating to the pipe organ, say editors atMerriam Webster Inc.
Each pipe in an organ produces one musical note. Usually at least three, but sometimes as many as 100 pipes in an organ play the range, from low to high, of a particular timbre or quality of tone. A set of such pipes is called a rank.
The organist sits at the organ console to operate the keybaords and foot pedals. Also arranged at the console is a series of knobs called "stop knobs" or simply "stops." Each stop controls the flow of air into a certain set of pipes so that the organist can choose the pipes within each rank to be played.
When a stop is pulled out, air will enter the pipes and produce sound as the organist operates the keyboard and foot pedals. When the stop is pushed in, no air enters the pipes and they are silent. The stops can be positioned before playing a piece or they can be changed in the course of playing.
If all the stops in an organ were pulled out, all the pipes would sound as the organist operated the instrument. The over-whelming blast of sound that would result is what lies behind our use of "pull out all the stops" to describe the unrestrained use of all available resources in attempting to accomplish something.