A GPU is a many, smaller processors operating simultaneously in parallel.
Each processor contains a lot of transistors. Many processors in parallel means even more transistors.
Every time each transistor switches, it must charge or discharge a parasitic capacitance inside the transistor. So the more often a transistor switches, the more often this capacitance is charged/discharged which means the more power is consumed. GPUs run fast so they switch very often.
So the fact that GPUs contain many transistors switching at the same time (because it's not just one processor operating at any one instant, its many processors operating at any one instant) and switching very often means very high currents to charge and discharge all those parasitic capacitors simultaneously.
A normal processor is more complex and has more transistors than than any single processor inside a GPU since it is has higher functionality, but it is also doing only one or two things at a time so only a small fraction of the transistors are switching at any point in time.