In-universe, the explanation has always been vague, but as others have pointed out, the plunger has proved to be very much a multi-tool for the Dalek using it. Much like the sonic screwdrivers, it is given whatever function the writer wants it to have, so in-universe, it is an almost impossible combination of devices all rolled into one "manipulator arm", as was referred to on screen.
There have been numerous single-use devices used in place of the manipulator arm/plunger over the years, including blow torches, claws, cutting tools, syringes, and scanning equipment. The default plunger-like form implies it is the most versatile form. What is covered by the plunger prop is enough to explain a lot of functions that wouldn't make sense if they merely had a claw or mechanical hand.