The observation that eventually lead to the kinetic theory of gases was Brownian motion. In the original experiment in 1827 Brown observed pollen grains in water and saw tiny particles dancing around without any apparent cause. In gases we demonstrate the same sort of thing by looking at smoke particles in air. The complete explanation that the molecules of any gas, such as in air, are in constant and very fast motion, had to wait until 1905 when Einstein explained that it was fast moving molecules hitting the particles so hard that they jumped or vibrated.
The fast motion of the molecules explains diffusion, which is the spreading together of two different liquids or gases. For example if you gently pour some sugar into a drink without stirring it and taste it immediately then you cannot taste it. Leave it for an hour and you can taste it easily. The spreading of the molecules of sugar is slowed down by their repeated collision with water molecules. A stink bomb let off on one side of a room can quickly be smelt on the other side because the molecules of the gas (hydrogen sulphide and ammonium sulphide with others) are moving fast and quickly spread.
Below is a short video of Brownian motion observed together with explanation.