Leverage
The pedal is designed in such a way that it can multiply the force from your leg several times before any force is even transmitted to the brake fluid.


Force multiplication

In the figure above, a force F is being applied to the left end of the lever. The left end of the lever is twice as long (2X) as the right end (X). Therefore, on the right end of the lever a force of 2F is available, but it acts through half of the distance (Y) that the left end moves (2Y). Changing the relative lengths of the left and right ends of the lever changes the multipliers.