How it occurs Edit
Brownian motion happens when particles that are free to move around and collide with each other, making them both bounce off in different directions. Many of these collisions occur to create the random paths that the particles take. It occurs when gas particles spread out, a random and erratic motion.
As an example, observe the movements of pollen grains in water. If viewed under a microscope, you will see that they move around in completely random and erratic paths. What is happening is that the much smaller ,and more numerous, water molecules are constantly bombarding them from all sides. More water molecules hitting the grain on one side than any other side produces a resultant force and the grain is pushed in that direction. This happens many times so that the grain follows a random path.