Currency

All copper, silver, electrum, gold, and platinum coins on the Prime Material plane originated in a dragon's hoard. Dragons are the native dominant creatures of the Magic plane. These coins are essentially crystalized magic. This is why some spells that have a material component have specific cost requirements, and also explains how prices have remained stable for millenia. If you were to stand silently in a dragon's hoard, you would hear the distant clinking of new coins appearing and dropping onto the pile, always somewhere just out of sight.
These coins are lighter than the non-magical metal versions in the Mundane world. They cannot be destroyed or even damaged by non-magical means. If powerful enough magic is directed at a coin it may "destroy" it, in which case the magic is simply released into the ambient magic of the world until it eventually crystalizes as a new coin in a hoard. These magical metals do not exist on the Prime Material plane as naturally-occuring ores. Their place is taken by ores that cannot exist on the Mundane plane, such as mithral, adamantine, arandur, and telstang.
The one way these metals can be modified from coin form is by magical crucible. Copper, silver, electrum, gold, and platinum can all be melted down and applied to weapons, armor, and magical items. Silver is the most well-known, as it has somehow entered common knowledge that silvered weapons are effective against lycanthropes when little else is. It turns out they are also useful against devils. Far less commonly known is that gold-plated weapons have a similar effect on demons, and that electrum can be used against yugoloths. Practically no one is aware that copper- and platinum-plated weapons are damaging to certain celestials. Like lycanthropes, various creatures of the material plane are similarly affected by particular metals.
Coins leave hoards and enter circulation when a dragon spends them, perhaps by hiring adventurers to do something or just polymorphing into a humanoid and going to a market. It also occurs when the coins are stolen – dangerous, but lucrative. Finally, when a dragon dies, many of the protections on its hoard die with it and the money becomes available to whoever can carry it away. An undiscovered horde will gradually dissolve back into ambient magic.
It is extremely dangerous for anyone other than a dragon to hoard wealth. Dragons are beings of almost pure magic and their connections to their hoards are unique. If a mortal accumulates a great deal of money, they risk developing what is sometimes known as dragon sickness. They become obsessed with it, wanting to accumulate more and more through any means necessary, almost as if trying to replicate the nature of a true dragon's hoard to grow itself.
Thieves occupy a critical niche in the world for exactly this reason. Wherever wealth starts to accumulate, thieves are there to redistribute it. While the individual being robbed may not appreciate it, society as a whole learned long ago that things work out much better this way. This is why there has never been a concerted effort to stamp out thievery, and why thieves can act almost openly to the point of having their own guilds.
On the Mundane plane, humans had access to the raw metals, as heavy ore instead of magically imbued coins. They instinctively understood that it had value, but couldn't access the intrinsic magic that is fundamental to it on the other planes. This led to such rationalizations as "gold is valuable because it is beautiful" (despite humans not valuing other beautiful things so highly, such as unpolluted nature or peace), or "gold is valuable because it is rare" (despite humans not valuing other rare things so highly, such as potable water or endangered species).
Since the Convergence, humans have begun to introduce capitalism into the Mundane plane. Some of them are accumulating wealth, and worse, they have also introduced police forces to protect it from thieves. This has not yet built to a disastrous level, but the danger is growing.

Manifestation

The coins take physical forms that are representative of dragons. Copper coins take the shape of the scales of the dragon whose hoard they appear in (albeit smaller). Silver coins take the form of the dragon's tongue, and gold coins its fangs (not so sharp as the real thing, so one needn't worry about gold coins poking holes in one's coinpouch). The much rarer electrum coins approximate the shape of the dragon's wings. Finally, platinum pieces are the only ones that are round like most Mundane coins, and also are not a single uniform color. They appear as a metallic version of the dragon's eye. Thus the coins represent the defensive armor, speech and spellcasting, destructive power, speed and mobility, and knowledge and wisdom of the most magical creatures in existence.
Common names are as one would expect: scales, tongues (or silvertongues), fangs, wings, and eyes.

Localization

Coins of any value might appear in any hoard, but copper is far more likely in the hoards of very young dragons and platinum is more likely in those of ancient dragons. Since not all dragons survive to become ancient, this explains the fact that coppers are so much more common than platinums. (Although their values would remain consistent even if there were orders of magnitude more platinums in ciculation than coppers; it's a measure of the magic imbued in them, not their relative rarity.)
All coins of a certain type are equivalent to all others. Sizes and shapes vary according to the dragon whose hoard the coin orginated in, but are always similar: a young dragon's copper scale coin is only slightly smaller than an ancient dragon's copper coin, even though the actual scales themselves are enormously different. The size difference has absolutely no impact on the value, a copper is a copper.

Type

Metaphysical, Arcane