Brownian motion is used to refer to the random motion of microscopic particles in a fluid. The motion is random because the particles collide with the atoms and molecules. The name comes from a botanist, Robert Brown, who observed such motion first while observing the movement of microscopic starch grain particles inside a pollen. This observation later led to the confirmation that any matter is made up of atoms, by Albert Einstein and Jean Perrin.
For perspective, remember that temperature is a measure of the motion of atoms... and using an absolute temperature scale, room temperature is about 298C. In other words, it's pretty hot, meaning molecules are moving around very, very rapidly. As smaller molecules, such as water, collide with larger ones, the direction and energy of the collisions will be random and thus the larger molecules "bounce around" at the hands of an "invisible" but energetic force.
According to the book "Bee in a Cathedral", the average speed of a water molecule at room temperature is 650 m/sec: pretty incredible for a chunk of matter consisting of three atoms!
Frequently Asked Questionsedit
Brownian motion is simply an extension of a random walk that is scaled with time. So a random walk is usually considered as a discretization of a Brownian motion.