What are these "pimples" on the jet engine for?
They are the roots of the variable stator vanes that control the direction of the airstream as it enters each compressor stage to manage and optimize the angle of attack of the compressor blades in each stage.  The vanes are connected to the ring shaped gang bar and somewhere around the circumference there is an hydraulic actuator, or a series of them, that drives the gang bar rings to move all the vanes connected to it at the same time.  The hydraulic actuator is usually powered with pressurized fuel and is operated by the fuel control system to keep the vanes at the optimal rotational position.

This video (thanks, @Mackk) shows how the vanes operate: