Fiat Money is money whose intrinsic value is minuscule (unlike, say, gold coins), but which has been declared by a government to have value as legal tender for all debts within the nation that issues the currency or coin. Fiat currency is problematic, even in an honest system, because it requires a strict overseeing operation to ensure that none of it is put into circulation at face value illicitly.
In a fiat monetary system the central bank is empowered to obtain the printed notes at the cost of production and then issue them into the money supply of the nation at face value (by exchanging them for reserve deposits of the authorized requesting commercial bank). It must also retain the reserve funds received in the exchange as collateral. This collateral is ultimately needed to redeem the cash being returned by a commercial bank for credit to its reserve account at the central bank. Upon the return of cash to the central bank, the face value is credited to the reserve account of the submitting bank, and the collateral account at the central bank (a liability account) is debited by that amount. At this point the returned notes have, by law, an accounting value of $0 on the central bank's books. The central bank then places the paper notes returned in good condition in a vault for a later demand and destroys those in bad condition. There is no profit made by the central bank as this scenario plays out.
For the case of the United States' fiat-money system this is verified in the following quotation from http://www.treasury.gov/resource-center/faqs/currency/pages/legal-tender.aspx
Federal Reserve notes [herein called FRNs] are legal tender currency notes. The twelve Federal Reserve Banks issue them into circulation pursuant to the Federal Reserve Act of 1913. A commercial bank belonging to the Federal Reserve System can obtain Federal Reserve notes from the Federal Reserve Bank in its district whenever it wishes. It must pay for them in full, dollar for dollar, by drawing down its [reserve] account with its district Federal Reserve Bank.
Federal Reserve Banks obtain FR notes from our Bureau of Engraving and Printing [BEP]. It pays the BEP for the cost of producing the notes, which then become liabilities of the Federal Reserve Banks, and obligations of the United States government.
Congress has specified that a Federal Reserve bank must hold collateral equal in value to the Federal Reserve notes that the bank receives. This collateral is chiefly gold certificates and United States securities. This provides backing for the note issue. The idea was that if the Congress dissolved the Federal Reserve system, the United States would take over the notes (liabilities). This would meet the requirements of Section 411, but the government would also take over the assets, which would be of equal value. Federal Reserve notes represent a first lien on all the assets of the Federal Reserve banks, and on the collateral specifically held against them.
This article will show how each transaction in the journey of FRNs from the cradle to the grave alters the balance sheet of each of the agencies involved in each transaction.
Some folks discussing money on the www think that the Federal Reserve pockets the seigniorage on transfer of FRNs from the Bureau of Engraving and Printing to the member commercial banks of the Federal Reserve. It will be shown that there is no such profit made in the process.
The term, "seigniorage", is defined  as "the difference between the [face] value of money and the cost to produce it - in other words, the economic cost of producing a currency within a given economy". This term is misunderstood frequently. It is sometimes used to encompass all income (imagined or actual) accruing to the Federal Reserve banks, their member commercial banks, or the US Treasury. This would include not only an allegation that the Federal Reserve pockets seigniorage on the FRNs printed at a cost of a few cents each and valued in the economy at full face value, but also interest made on bank loans. This is wrong. Seigniorage is simply a noun defined strictly as stated above. It carries no implication of profit; it is simply a mathematical difference between face value and cost. Interest on loans has nothing to do with it.
If the agency that provides the currency to commercial banks, be it a central bank or the government, is permitted to pocket this difference, then there is profit made on the seigniorage in supplying currency. If this is the law, then from the providing agency's perspective it is a pure sale with no implied requirement to redeem currency at face value ever. Such currency would not be legal tender for all debts public and private, because the initial supplier will not accept it as a bank deposit or as payment for any debt. It is sold by the authorized agent once, and all subsequent transactions are between private parties--provided the public perceives value in these notes. (And why would they see value in them if the central bank won't redeem them?)
In the case of the US Federal Reserve (FR) monetary system all outstanding currency in the hands of the public is, by law, a face-value liability of the FR and an obligation of the US government.
Understanding the mechanics of FRN transactions
It is helpful to use double-entry accounting T-accounts to illustrate the transactions involving currency and understand their implications within our FR monetary system. As transactions occur between two entities in the system, the balance sheets of the two (among the FR, the US Treasury, the commercial banks, and the checkable bank accounts of the public) change from one balanced state to another. The balance sheet of an entity has two columns. The left column lists assets, and the right column lists liabilities. The sum of the assets must equal the sum of the liabilities. The booklet, Modern Money Mechanics, published in 1961 and still available here: http://lisgi1.engr.ccny.cuny.edu/~makse/Modern_Money_Mechanics.pdf, shows how T-accounts are useful in this kind of analysis. The approach taken in this article illustrates the changes in balance sheets that occur when FRNs change hands as the FRNs proceed from printing to final destruction at the end of their useful life.
Birth of FRNs