The relevance of the boiling point of brake fluid One is told to change the brake fluid because it attracts water. The water lowers the boiling point of the brake fluid which, I am told, reduces the efficiency of the brake fluid.
What is the relationship between the boiling point and the transfer of mechanical energy to the wheels?
 A: Brake fluid can get really hot because brakes get really hot and some of the fluid is very close to those hot parts.
Brake fluid works as a liquid rod: when you push on one end of the brake pipe it pushes on the other, since it is essentially incompressible.   The advantage of a fluid-based (hydraulic) system over using actual rods is that it's much easier to ensure that all the brakes get equal force, since the pressure is the same in the whole system is the same (I have a car with rod brakes and stopping is exciting in bad ways).
If the fluid boils then the system stops acting like a rod: suddenly there is extremely compressible vapour in the system, and the action of the brakes becomes only faintly related to the movement of the pedal.  This is a bad thing, and is exactly the same reason you don't want air in brake lines, of course.
At first blush this seems like a non-problem however: if the fluid boils then, since the system is already filled with fluid, and sealed, the worst that would happen is that the brakes would stick on a bit due to some extra vapour.  But in fact the system is not sealed all the time: when the brakes are off there is a reservoir of brake fluid which can 'see' the system through a small hole, which is uncovered when the piston in the master (pedal) cylinder is right back.  The purpose of this is to deal with slow leaks and changes due to temperature.  But if the fluid is boiling near the brakes, a lot of it will be forced out into the reservoir, leaving the braking system itself full of a lot of vapour.
