The participants are time-and-space separated buyers and sellers of
- Commodities like wheat, barley, cows, coal, electricity and so on
- Money itself, in which case we call this lending and borrowing
- Money for other money, commonly called currency transaction
- Ownership stakes in companies, aka shares
- Contingent claims like options and futures on the above
Say you want to build a factory to make cars. That's going to cost something, and you want to share the risk with the public.
- When you IPO this company, you get a bunch of money from the buyers of your shares. The owners of the shares, why do they bother? They don't just get all the profits of the company like if they owned a restaurant. They don't control the car factory, they leave that to the management, including how much of the profits are paid out. What if they need the money, despite everyone thinking the company has good prospects? Enter the secondary market, what we normally call the stock market. Here you can find other people who want the shares you don't want, and will give you money today for your shares, even if the company hasn't made a dime yet.
- You have plans with the 10B from the IPO, but not right this day. If there were a money market you could gather some interest until the bill for the factory comes. Some other business needs to make payroll with their receivables a couple of weeks later. You just need to match with them somehow.
- When you start selling cars, you find that a lot of people don't have 50K in cash. Not to worry, you hand these people their cars anyway, and you make a financing plan where they pay for the car with money that they owe you. Now you have a bunch of loans from people, but you can't use the IOUs to expand your factory. What do you do? You find someone to forward you some actual cash on the expectation that the car buyer will eventually give you the money for the car. You just need a market to find this person with the opposite need to you.
- You might sell cars in other countries. If your factory is not in that country, your expenses will be mismatched. If only there was someone out there willing to swap all the Euros you got from selling cars in Europe for your Dollars that you use to pay your workers. It happens that there are other companies in America expanding to Europe needing Euros for their local offices, and having only dollar income. How to find them?
So what happens then? Who is going to match all these different interests? The answer is market makers. Basically people who know that there are clients whose interests match. Your basic middle man who stands there when the farmer comes in, buys the grain, and then waits for the restaurant guy to come in, and sells them. That way they don't need to meet at the same time and place, and they don't need to match exactly.
Not matching exactly brings us to contingent claims. If everyone just transacted everything in the exact right quantities, that would be nice for the market maker. He'd just take a spread on everything and sleep comfortably. But that's not what happens and supply and demand change, and prices change. In fact prices can change a lot, and you might need some sort of deal where you can buy or sell something, but only if the price is at some particular level. Or you might want to buy or sell something definitely, but not right now, only at some time in the future. This whole derivative game allows people to move risks around in order to match their changing balance of buyers and sellers.
I haven't even added speculators yet, but that's the start of a "who/why markets" answer.
EDIT. I know people will ask next. What does any of this very nice sounding imaginary world of completely explicable financial needs have to do with arbitrage?
The answer is liquidity aggregation on similar products, and liquidity spreading by interaction of participants.
Let's say there's a market to borrow money for each year in the future, eg 2024, 2025, 2026, and so on. Some guy decides he needs to borrow money for 2025 to build a factory. As a market maker, that's fine, but hey wait a minute. There's nobody I know who wants to lend in 2025. What do I do? I have this guy who wants to lend in 2024 and a guy who wants to lend in 2026. Hey, maybe I can just do all these deals, paying me a spread? My books will be slightly off balance, but don't interest rates basically move up and down together? Let's do it and deal with the mismatch later. So now these related markets are connected. They are sort of one large pool of liquidity, but still their own separate pools since there is still some difference.
This is a loose arbitrage. You're not guaranteed to make money on it, since rates can move the wrong way for you. But this is also the most common arbitrage, the one where you sort-of hedge your book against similar things and hope the imbalance falls out eventually.