'Representative Money' is explained in detail and with examples in the Economics edition of the Herold Financial Dictionary, which you can get from Amazon in Ebook or Paperback edition.
Representative money refers to any form of exchange that stands for a backing store of value. Yet this representing money itself usually has little to no value intrinsically, or by itself. This is a different concept from fiat money which might or might not possess a valuable store underlying it. For money to be legitimate representative money, it must have a valuable asset or item underlying the face value it carries.
Throughout history, representative money actually goes back further than even the use of coins. In ancient Babylon, Egypt, China, and India, palaces and temples maintained warehouses of commodities. These would issue deposit certificates as proof of a value claim on some of the goods kept in the warehouse. This made the certificates for deposit a true and very early form of this representative money.
In 1875, William Stanley Jevons the economist wrote that such representing money became popular as a result of the practice of noticeably clipping or depreciating the value of metal coins. When the precious metal coins remained in banks to guarantee their genuine physical value, these representations ensured the worth of the money. He reaffirmed the historical tradition of utilizing both paper and other forms of materials as representative monies.
Subsequently William Howard Steiner the economist write in 1934 that the phrase for representative money signified that a particular quantity of bullion was on storage with the U.S. Treasury. The paper bills which were circulating represented this bullion.
This term has also been extensively utilized to refer to money which was backed by a commodity like silver or gold. This existed in the United States as silver certificates or gold certificates. The original British pounds were redeemable for their face value in pounds of silver at the Bank of England. Later gold on demand from the BOE came to back these.
Representing money can also mean an item (that is not currency) which pledges the presenters’ intention to settle a debt or pay for a good or service. Checks which investors write to make deposits in Forex trading accounts against their own checking accounts represent a typical deployment of this kind of representative monies. It proves the holder wishes to pay for an item, and it can be easily changed for the underlying fiat cash money.
Fiat money should never be confused with representative money. This is because it is paper money and coins with nothing backing them whatsoever. The only reason such money holds any value at all is because people choose to accept the nebulous promise from the government that they will back it with their full faith, credit and trust.
Representative monies on the other hand represent the pledge to pay real money back. While fiat money is only backed by promises of governments, representing monies could be backed up by a wide variety of things. Personal checks are representative for promises to pay the check from underlying money in a checking account. The fact remains that such money needs backing to have any value at all. This gives it some similarities to fiat money, which relies entirely on the promises and backing of a sovereign government for any and all of its value.
The days when people could take their paper certificates or bills to a bank and change them for something valuable such as silver or gold are long gone (since 1971 in the United States). Bills are no longer restricted in their printing by the amount of gold (or silver) which backs them. This gold standard system collapsed largely because the U.S. government gave into the temptation to overprint their paper money supply beyond the gold which backed it in their vaults.
It caused rampant inflation in the 1970s until people finally became accustomed to government creating new paper money out of thin air whenever it suited their purposes. The reality is that if the government were to fall on difficult times financially and fiscally, their much-touted fiat money (and its unprecedented experiment) would rapidly become worthless.