Brake booster plates are used to increase the rigidity of frame brazed-on brake mounting studs. When you pull the brake lever on a cantilever brake, the straddle wire, connected to the top of the arms, pulls the arms in together. When the brake pads grab the rim, the wheel is still in motion, with all of its weight and all of its speed.
The brake pads gripping the rim transfer the force to the brake arm and the brake arm begins to flex. The transfer distance between where the brake pad is connected to the brake and the cantilever mounting stud is fairly short. This leaves a brake arm that is short and incapable flexing much, so when the brakes are applied the energy, in the motion of the wheel mass, is transferred through the inflexible arm to the cantilever stud, (which is only brazed onto the frame). This energy works separately on each stud, to try to rip them off the frame.
The bridge plates or booster plates reinforce the studs so they work together to dissipate the braking energy. Brake booster plates bolted over the brake to the mounting studs equalize the stress when braking, and thereby equalizes the quality of the weld or brazing that's used to fasten the stud. It actually lengthens the frame life, and helps to eliminate brake squeal and chatter.
To use the booster plate, the mounting bolts are removed from the installed brake and the plate is put in place over the mounting studs. Because the booster plate adds thickness, most of them come with a set of longer 6mm by 1mm threaded bolts used to bolt the plate and brake arms in place.