What is the purpose of the cylindrical layered conical discs in power stations?
These 'stacked cyclindrical discs' are all INSULATORS, which are used to  provide adequate CLEARANCE and CREEPAGE DISTANCE between high-voltage parts and earth.

CLEARANCE is the shortest distance in air between two conductors. Air is an insulator with an insulation value measured in kV/mm. You have to provide enough clearance between parts so that arcs don't jump through the air between parts.

CREEPAGE is the shortest length along a surface between two conductors. The surface of an insulator gets contaminated with water, dust, salt, etc. which is conductive. You have to provide enough "creepage distance" along the surface of the insulator, so that the electricity doesn't track through the water, dust, salt etc. and start arcing.

The shape is to maximise the creepage distance (along the SURFACE of the insulator) and to break up the flow of water along the surface. (If you had a simple cylindrical insulator, one rivulet of rainwater from top to bottom would cause an arc!)







When there's nothing inside the discs, they're called 'insulators'.
The brown discs in the photo above are insulators.
For transmission line use, you usually get individual discs and link them together into 'strings'. The more insulators in the string, the more voltage it can withstand.





In the photo above, the insulator is part of something else.

The photo above is of a current transformer - a device for measuring large currents (at high voltage). The circuit being measured might carry 2,000 amps at 132kV. The current transformer would scale the current down to 1 amp for measurement purposes.

The insulator is required to isolate the 132kV conductors at high voltage, from the measurement circuit at low voltage.