What are these spinning discs next to the throttle of the Boeing P-8 Poseidon?
Those spinning discs on either side of the throttle quadrant are the stabilizer (stab) trim wheels.

The stab trim system can be actuated by electric trim switches on either the left or right control yoke, the autopilot (AP), or by manually turning the stab trim wheels. The yoke mounted electric trim switches "spin" the trim wheels at the high speed seen in the GIF above, while the AP turns the wheels at a relatively slower rate. A stowable handle in the trim wheel can be pulled out to allow for faster manual turning.

I've heard that this handle can be very painful to the knees if left unstowed and either the AP or especially the electric trim turns the wheels.

See "Why I hate the Boeing 737" for more info on the system, including photos of the trim wheel and stowable handle: