Pascal's law states that when a fluid is kept in a closed container, the pressure at one point will be equal to every other point on the fluid.
We know that pressure is force per unit area.
In hydraulic brakes, when a small pressure is applied to a small piston with a smaller area, this pressure gets distributed equally throughout the entire fluid.
On the other end, a piston with a large area is present which experience this equally distributed pressure.
This exerts a huge force and a brake is applied.
Thus, the hydraulic brakes are based upon Pascal's law.