Alright, let's start with precious metals and work forward from there. As a species, we've recognized the value of gold and silver, and copper to a lesser-degree, for a long time - about 40,000 years. The reasons should be pretty clear. They're visually appealing, visible in small amounts on the surface or easily accessible beneath it, and easy to work with. The big benefit for value is not only were precious metals rare in those circumstances, but have remained rare as our methods for extracting them have advanced. So, intrinsically, gold and silver are desirable, useable and rare and thus have higher value than many other things.

That was the basic case throught the Neolithic Period, the Bronze Age, and the early Iron Age. Once bronze was in regular use it mostly supplanted copper in the hierarchy of valuable metals. By the middle Bronze Age you start seeing regional standards of ingots and bullion in the Near East/Aegean. Obviously precious metals need to be transported and having a standard of exchange makes trade and payment easier.

Speaking of payment, that was one way of paying for things at this point: a certain number of metal ingots. They were valued based on weight and purity, which corresponds more or less to how much gold/silver/bronsze product you could get out of each ingot, and that metal value had an understood exchange in a market. On the other hand, it was still very common to pay for services in kind with grain, wine, or other provisions. So mercenaries in the Bronze-Iron Age periods were probably paid in rations and housing (in addition to their plunder, land grants, or whatever else could be acquired in a campaign). Truth be told, we don't know much about mercenaries prior to Classical Greece.

Jump forward to the mid-6th century BCE and you finally get the big change. Somewhere in the Aegean Sea region, somebody started minting little medalions with their/their city or kingdom's emblem on them. Who exactly started this is unknown. Traditionally, it's thought to be King Alyattes of Lydia, but Greek kings/tyrants on some Aegean islands were doing it around the same time.

These medallions were mostly just symbols of royal favor, but when they became numerous people started exchanging them for their metal value in the marketplace. They were like smaller versions of ingots. If you knew the weight and purity standard that was in use where those medallions were minted, you could reliably know how much they were worth on site. The thing is, those standards weren't formal yet and gold and silver was still pretty rare in day to day use so they were too valuable to use for most transactions.

The first king we know to have instituted a strict standard was Croesus of Lydia. He produced silver and gold coins called croeseids that had a very reliable weight standard. The idea spread quickly throughout the Greek world. When Croesus was defeated by Cyrus the Great and Lydia became part of the Persian empire, croeseids remained in use until Darius I the Great instituted a new standard for the Persian Daric that had wider circulation.

However, it took about a century for coinage to really catch on in the Near East, where it continued to trade purely on the value of the metal. It was really in Greece where it took off. The base unit there was the drachma, and different Greek cities had different standards, but Athens eventually emerged as the most common and reliable standard over the course of the 6-5th century BCE.

Because of Athenian trade dominance in that century, many cities adopted their standard and cities that wanted to compete with their own standard became more rigorous. In that setting, coinage was becoming more widespread, had a very reliable value, and was easier to carry around than large ingots of bullion or hauling jugs of olive oil to barter with. Before long, extremely small denomination were being minted to make coins for smaller purchases because it was so convenient (some coins smaller than a pencil eraser). It was convenient, reliable, and it quickly became the preference for merchants and buyers alike. Somewhere in there, coinage made the jump to having psychological value slightly higher than the metal value because it was more convenient and more widely accepted than just a lump of metal.

The boom in mercenary activity came about a centurt after the boom in coinage use. Up to about 430 BCE the order of the day in Greece, Egypt, and Persia had been locally levied troops. Sometimes Egypt hired Greeks to come in a bolster their army or occupy garrisons when their was tension between the Pharaoh and local troops and the Greeks might hire specialists like Cretan archers that had skills rarely found in their normal levies.

That changed in the aftermath of the Peloponnesian Wars and the succession crisis in Persia after Artaxerxes I. It's the Greek side of things that's most important here. During the Peloponnesian War, the political system in Greece was reorganized around powerful hegemons. There was rapid political reorganization, not just in the main powers of Athens, Sparta, and Thebes, but in the smaller city states that shifted alliances between them. There were also near constant wars between different alliances that drew on much larger armies than prior wars.

That created a lot of polticsl unrest and economic disasters as crops were burnes and neglected. On top of that, grain from the Black Sea, Syracuse, and Italy was doing really well and could actually out price local grain in Greek markets. Greek farmers trying to stay profitable had to diversify their crops, which, was difficult, exppensive, risky, and didn't always work. Many people became poor and somewhat desperate for work.

The Peloponnesian War also drove a demand for peltasts. These were lightly armored infantry that protected the flanks of a phalanx and could be deployed in more treacherous terrain. They're equipment was also cheaper and could be supplied to men who could not afford their own hoplite armor. They started as mercenaries brought in from Thrace to bolster Athenian numbers in the Peloponnesian War, but Greeks quickly started adopting their tactics as a role for men who couldn't afford to become hoplites.

It turns out, being a successful peltast required more practice and skill than being a hoplite in many situations. The whole point of the hoplite phalanx was that farmers could learn to fight in formation quickly, but the looser formations of peltasts were better suited to full time soldiers who could really hone their role in battle. In the Persian Empire and Egypt they had no heavy infantry and took to hiring Greek hoplites looking to make some extra money or get military experience for garrison duties, to form rebel armies, or to counter hoplites in enemy armies.

Both Greece and the Near East spent the 4th century fighting and that drove up demand for mercenaries. Plus there was Dionysius the tyrant of Syracuse in the west also hiring Greek soldiers wherever he could.

At the same time, Greek trade and the Persian Daric were starting to influence Egypt and the Levant and coinage was coming into more common use there as well. Coins were the basic medium of exchange in all of the places employing mercenaries and were preferred in the markets for all of the reasons above.

It's possible that the increased use of coinage by Persia, Macedon, and Syracuse pouring into Greece inadvertently triggered inflation and drove up the number of men seeking mercenary work.

Mercenaries were paid in coin at that point because it was the standard that was easily identified and agreed on by mercenaries and their employers. It was also easily transported and moveable, unlike additional supplies and rations, and could be used to purchase from local towns as the army traveled, often stimulating the economy of their employer.

They were paid in coin slightly more often than other professions because they had to be mobile whether or campaign, going to a new job, or making their way home and like this all started, coin was convenient and mobile.

I literally just wrote a paper and finished a class on this, but might need a bit more context to turn it into an answer. What period and place are you asking about?