Argon is a noble gas, and the only one that we encounter in sizable quantities around us regularly. Argon makes up about 1% of the atmosphere around us, depending on whether it is calculated by volume or weight. Considering the amount of breaths we take every day, we have a lot of argon passing through our lungs. The lighter noble gases, helium and neon, are too light to stay in the earth's atmosphere. The heavier noble gases, krypton, xenon and radon, exist in too small of quantities to play much of a role in our atmosphere.
Of the argon in our atmosphere, almost all of it was generated by the radioactive decay of Potassium, specifically the Potassium-40 isotope. Although the history of the earth's early atmosphere is somewhat hazy, any gases that were present when the earth originally coalesced were quickly driven off by its heat and repeated comet strikes. The atmosphere that now exists was released slowly, over time, from vulcanism. The argon that exists in earth's atmosphere is argon-40, and is heavier than the argon that exists in most of the universe, which is argon-36, and is formed from stellar nucleosynthesis. The amount of potassium in the earth's crust is small, the amount that is the potassium-40 isotope is even smaller, and the amount that decays into argon is even smaller. However, the earth is big and dense, and argon is a diffuse gas, so the volume of argon that can be created by the potassium trapped in the earth can be quite massive. There may be hundreds of cubic miles of argon still waiting to be released, trapped deep in the earth. Whether this is so is left as an exercise to the reader.
Despite its great commonality, argon plays little direct role in the chemical interactions between the atmosphere, ocean and biosphere. Argon is a noble gas, meaning that (except in some extremely complicated laboratory conditions), it can not form compounds with other chemicals. It is totally inert. This is in contrast to the molecular nitrogen that makes up 78% of the atmosphere, which is an inert molecule, but can be broken down and turned into compounds under the right conditions. The closest argon comes to forming compounds are clathrates, structures where the argon is trapped in a lattice of other molecules while not actually being bonded to them. There is, for example, an argon-ice clathrate. However, under standard earth conditions, these compounds are not very common. On another planet, argon ice and seas of liquid argon might play an important role. Argon also plays a role by its lack of role: since it is totally inert, an argon atmosphere would stop almost all chemical reactions inside of it. It is used in industrial processes on earth for that purpose, and logically, it would follow that the 1% of argon in our atmosphere means that fires burn 1% slower than they would without that argon. Perhaps in some distant future when the volcanos have indeed belched out hundreds or thousands of cubic miles of hidden argon, the earth will be blanketed in an inert atmosphere, with metabolism stopped, and everything preserved.
One of the differences between chemistry and math is that in chemistry, a bunch of nothing can add up to something. Although 1% of an inert gas might not seem like much, other trace gases present in even smaller quantities, such as carbon dioxide, ozone or nitric acid can play in atmospheric processes. There may be some obscure and important role that argon plays in our atmosphere, or that it may play in the atmosphere of exotic exoplanets, that is not immediately obvious.