Question

What is diffusion and Brownian motion

Answer 1

the intermingling of substances by the natural movement of their particles.
the erratic random movement of microscopic particles in a fluid, as a result of continuous bombardment from molecules of the surrounding medium.

Answer 2

Brownian motion is the stochastic motion of molecules. As given by the kinetic molecular theory, the direction of motion of molecules is random. 

Diffusion is a statistical phenomenon one observes, due to Brownian motion. The random movement of molecules ensure that a molecule will travel from its starting place, in what's called a "random walk" pattern.

Diffusion isn't EXACTLY random movement. It's usually movement of particles from areas of high to low concentration. Brownian motion, on the other hand, is completely random.