The idle stop solenoid is used to temporarily hold the throttle valve open when letting up on the throttle. It is also used to set the idle speed. These are all but impossible to find these days, so remove it and replace with a bolt you can adjust by hand.
An idle stop solenoid is used to control the idle. The solenoid is electrically controlled through the ignition switch. When the ignition switch is turned off, the solenoid is denergized, allowing the carburetor throttle valve to close further, preventing the engine from running after the ignition switch is turned off.
As of this writing the solenoid is not being produced anymore.