Following that thread led to this fascinating information (at least to me). All courtesy Wikipeadia.
Robert Brown FRS (21 December 1773 – 10 June 1858) was a Scottish scientist who is acknowledged as the leading botanist to collect in Australia during the first half of the 19th century. He also is credited with the first observation of Brownian motion.
In 1827, while examining pollen grains and the spores of mosses and Equisetum suspended in water under a microscope, Brown observed minute particles within vacuoles in the pollen grains executing a continuous jittery motion. He then observed the same motion in particles of dust, enabling him to rule out the hypothesis that the effect was due to pollen being alive.
The Roman Lucretius's scientific poem On the Nature of Things (c. 60 BC) has a remarkable description of Brownian motion of dust particles. He uses this as a proof of the existence of atoms: "Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e. spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible." Although the mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is indeed caused chiefly by true Brownian dynamics.
Consider a large balloon of 10 meters in diameter. Imagine this large balloon in a football stadium. The balloon is so large that it lies on top of many members of the crowd. Because they are excited, these fans hit the balloon at different times and in different directions with the motions being completely random. In the end, the balloon is pushed in random directions, so it should not move on average. Consider now the force exerted at a certain time. We might have 20 supporters pushing right, and 21 other supporters pushing left, where each supporter is exerting equivalent amounts of force. In this case, the forces exerted from the left side and the right side are imbalanced in favor of the left side; the balloon will move slightly to the left. This type of imbalance exists at all times, and it causes random motion of the balloon. If we look at this situation from far above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.
Considering Brown's pollen particle moving randomly in water: we know that a water molecule is about 0.1 by 0.2 nm in size, whereas a pollen particle is roughly 25 µm in diameter, some 250,000 times larger. So the pollen particle may be likened to the balloon, and the water molecules to the fans except that in this case the balloon is surrounded by fans. The Brownian motion of a particle in a liquid is thus due to the instantaneous imbalance in the combined forces exerted by collisions of the particle with the much smaller liquid molecules (which are in random thermal motion) surrounding it.