This video shows how a click pen works from inside.
when you push the back button ,it actually pushes another part called thrust device or cam piece which pushes the ink cartridge forward, thus ball point tip gets out from the pen nozzle. But for this mechanism a coil spring is very necessary. coil spring stores energy when compressed and when push button is released, springs rebound force helps to complete the mechanism.
each time it makes click sound not ones but twice every time you press and release the click button.
Watch the animation and you will be able to understand the mechanism.
Thank you .