Torque arms are used to prevent axle rotation in hub motors. When a hub motor is powered up running, for all the torque that the motor generates spinning a wheel forwards, there is an equal and opposite torque on the axle causing it to rotate backwards.
In most electric bicycle hub motors, the axle is machined with flats on either side which key into the dropout slot and provide some measure of support against rotation. In many cases this is sufficient. However, in high power systems that generate a lot of torque, or in setups with weak dropouts, the forces present can exceed the material strength and pry the dropout open. When that happens, the axle will spin freely, wrapping and severing off the motor cables and potentially causing the wheel to fall right out of the bike.
To give a sense of the magnitude of these forces, a hub motor with a 12mm axle generating 40 N-m of torque will exert a spreading force of just under 1000lb on each dropout. A torque arm is a separate piece of metal attached to the axle which can take this axle torque and transfer it further up the frame, thus relieving the dropout itself from taking all of the stresses.
Rear bicycle dropouts are usually thicker and stronger than the front fork dropouts, so more often than not a rear torque arm isn't necessary. But in cases with shallow vertical dropouts, or with powerful (>1000 watts) motor setups, it can be as important as the front. Our Rev4 design uses multiple hose clamp slots to secure to the arm to a seatstay tube. The axle plate can flip directions to accommodate both horizontal and vertical dropouts, while the hose-clamp arm clears up and over most eyelet holes present on the rear.