What is this brake torque link?
What's it for?
The torque link arm is the hypotenuse (longest side) of a nearly-right triangle. The three points on the triangle are a torque link arm bolt on the swingarm, a torque link arm bolt on the brake caliper carrier, and the axle. (The caliper carrier also doubles as a rear-wheel spacer, so the axle goes through it.)
It keeps the caliper from spinning around with the wheel when the brakes are applied. The force of the spinning wheel wants to take the caliper with it when you use the brake. The torque link keeps everything in its place.
Why is the bike built this way? Simple. It maintains a constant relationship between the position of the brake caliper (attached to the swingarm) and the brake rotor (attached to the wheel).
For adjusting chain tension
So, the sides of the triangle are made up of part of the swingarm, the brake caliper carrier, and the torque link arm. When you adjust the rear wheel position (chain tension) you are changing one side of the triangle. Since the torque link arm and caliper carrier are of fixed length, simple trigonometry tells us that the contained angles must change (or something bends). Having all three triangle corners loose (two torque link bolts and the axle) makes changing the contained angles MUCH easier.
When you adjust your chain tension, you are actually changing the length of your wheelbase as well, albeit a small amount. With the top of the caliper held by the torque link, and the bottom bracket connected at the axle, by increasing your wheelbase you are moving the bottom of the caliper bracket back as well. Without loosening the top of the bracket (the torque link) and allowing the caliper to rotate just a teensy bit, you are stressing the connection at the top of the caliper.