Ok so I think I see where your confusion is coming from.
Any device has a set number of parts, be that resistors or capacitors or switches or transistors etc. And as far at the power supply is concerned that whole thing has an impedance. How much current the power supply must deliver, as you have mentioned, depends on the impedance. Lower impedance means it must supply more current.
So far so good.
So how does the impedance lower?
The impedance of a device changes depending on the particular state the device is currently in. Since devices have things in them that can change their state, like switches and transistors, that means they can change their impedance.
Lets paint a simple picture.
simulate this circuit – Schematic created using CircuitLab
You can see this device is just a lamp and a switch. It has two parts, but it's impedance seen to the power supply will change depending on whether the switch is open or closed. With the switch open, the impedance is pretty much infinite, with the switch closed the impedance is the resistance of the lamp. The constituent parts did not change, but their state did. As such the impedance of the device as a whole changed.
The same applies to all devices, be they simple lamps with one switch, or the computer I am typing this answer on with millions of transistors switching millions of times per second.
When busy, my computer is not using more transistors, it always uses the same amount, but rather more of the transistors it is using are switching on and off changing the systems impedance.