Brownian motion occurs when very small particles suspended in the fluid, seen under a microscope, appear to follow a zigzag trajectory of a totally random nature. Usually a phenomenon in science is not named for one who merely observes it, but is reserved for the person who provides a satisfactory explanation, or at least attempts one. But the English biologist Robert Brown had no explanation for what he saw in his microscope in 1827, when he was examining pollen grains suspended in water. As a biologist, his first suspicion was of animal motion, but he was able to rule this out when he observed the same thing with minute inorganic particles. This is as far as he went.
Neither was he the first to observe it. In 1785 the Dutch physician Jan Ingenhousz observed the same phenomenon with coal particles suspended in alcohol, and even as far back as the first century BC Roman poet Lucretius observed dust particles zigzagging in sunbeams, which is essentially result of the same phenomenon. In fact Lucretius was way ahead because he supplied an explanation too, which is largely correct. Mystical poet of the natural world, and well versed in his Democritus, he correctly surmised that it was the atoms (we would say molecules) that were pushing the particles around.
However, Brown's discovery was on the heels of John Dalton's revival of the atomic theory, which set into motion the stupendous scientific journey into the fundamental constituents of matter. It was also a mere nine years after the publication of Mary Shelley's Frankenstein, the definitive allegory of the grasp of modern science. We may draw a striking parallel between Victor Frankenstein's first observing his monster creation twitching into life, and Brown observing the twitching of the molecules, suggestive of the birth of modern science, even though it remained unexplained, and went largely unnoticed.
It was not until 1889 when French physicist Louis Gouy finally caught up with Lucretius, suggesting that it was the liquid molecules in motion that caused Brownian motion, so that the phenomenon finally clinched the evidence for the existence of molecules. He also noticed that smaller particles moved faster, and in 1900, Austrian physicist Franz Exner noticed that the speed was directly related to temperature. All these findings found a theoretical foundation through kinetic theory of gases.
In this theory, the molecules of gas move about randomly, and with various speeds. These speeds determine the temperature of the gas. In other words, temperature only expresses the speed of the molecules after it has been averaged out throughout the mass of the gas. When the molecules bounce off the container walls they exert pressure, which also averages out. The upshot is that all the classical gas laws find explanation through a model that is simple and intuitive. The kinetic theory of gases is a sublime triumph physics and chemistry. It comes about just by imagining the molecules moving about randomly - scientific imagination at its best.
Brownian motion is where imagination meets reality, but there are differences. Firstly, we are not dealing with a gas, but a liquid, where the movement of the molecules is not as free. Secondly, it is not the actual molecules that we observe moving. In other words, one molecule strike does not represent one pollen grain flying off in one direction. Each grain has millions of molecules striking in every direction. In the first instance it would appear that so many strikes should average out, so that the grain shouldn't move at all. But it happens that a few molecules have way excess speeds. These are the Hercules of the molecule world, and they manage to tip the scale one way or the other. The final effect: the spectacle of the molecules themselves in motion!