To start off, there does not have to be any notion of a standard paper or metal currency, whether it's fiat or backed by precious commodities such as gold, to tell this story. Why? The value of goods and services is largely determined by supply and demand, and even without an official currency as a reference to value transactions against, the value would still be expressible. A currency merely provides a standard against which to measure the value of transactions, and as such, it is a way to facilitate communications and transactions more efficiently. The value of a paper printed dollar does not lie in the paper or ink (or in the supposed backing by precious commodities), it lies in the communication of a transfer of goods and services; it is understood that the dollar represents some amount of past productivity that has yet to be compensated for (in the sense that there is no material benefit to the holder of a dollar until the dollar is exchanged for something else). Currency is like an IOU, and we just shuffle these IOUs around in exchange for goods and services. But if currency is like an IOU, then why not just use IOUs and forget about currency? In other words, why not just use credit instead of fiat money to facilitate our transactions? For private entities, if they issue too many IOUs (as if they were printing their own money, in a sense), then there is a real worry about the IOUs being redeemable in the future; if there's great difficulty in redeeming an IOU, then the IOU loses its value and possibly becomes worthless. It would be nice if there was an entity that could issue IOUs and guarantee that they will always be redeemable. The federal reserve does just that by issuing fiat money and regulating it with interest rates. How is fiat money issued? Through purchases, of course! So that I don't confuse things, from now on I will use the terms "currency" and "credit" to distinguish between transactions that don't have an associated interest and those that do, respectively.
Interest:
When the federal government (or the federal reserve) buys something, it can either use currency it has on hand, it can buy it with its own credit (what some people call "printing money"), or it can buy it with private credit (i.e. treasuries/bonds), and if it does the latter, the government becomes more indebted. Should we worry about the government being able make good on these debts? If the debt functions just like fiat money, then having more outstanding debt just means that there's more liquidity in the market, which could potentially have a large effect on the velocity of transactions and thereby economic growth. But debt typically has a rate of interest associated with it, which is potentially quite burdensome if too much of it is accumulated. At very low interest rates, government debt should be seen as nothing more than extra monetary liquidity, not much different than fiat money. As interest rates on government debt climb higher and higher, the debt functions less like money and more like a risky investment venture. Why risky? If there's a high demand for the debt, then the price of the debt increases and the interest on it decreases. If there's a low demand for the debt, then the price of the debt decreases and the interest on it increases. The level of demand is inversely correlated with the (perceived) level of risk. At little to no risk, and a corresponding little to no interest rate, debt functions very similar to fiat money. But if that's the case, then why wouldn't an investor just keep the money instead of loaning it to the government? Well, money just lying under a mattress tends to lose its value slowly over time due to inflation, and the little bit of interest on the debt helps to maintain the purchasing power of the investment. But the real reason to put money in an extremely low-risk investment vehicle is if the risk of all other investment vehicles exceeds an entity's risk-tolerance (or if it just wants to diversify and hedge its investments). The main point of this section is that credit at little to no interest is not much different than fiat currency, and it wouldn't matter if the actual currency had a hard standard or not, because the credit would still function as fiat currency.
Inflation:
A discussion of money is not complete without mentioning inflation/deflation. If inflation is zero, then what you can purchase with a dollar tomorrow is the same as what you can purchase with a dollar today. If inflation is positive, then you can purchase less tomorrow than today with a dollar. If inflation is negative (deflation), then you can purchase more tomorrow than today. Zero-percent inflation intuitively seems like it should be the most fair for everyone since regardless of what you decide to do with your money and when you do it, the money should have the same, constant utility (or purchasing power): you will be able to buy the same amount of stuff regardless of when you decide to buy it. Pragmatically, though, it turns out that zero inflation could potentially be a very bad thing. Why? It turns out that when private entities enter into deals with each other and sign contracts, they get locked into commitments that could potentially be very long-term. If there is deflation, then it makes sense for entities to save their money instead of spend it because that money will be worth more in the future than it is now. If many entities start saving money instead of spending it, then liquidity is removed from the market, the velocity of transactions slows down, demand for products and services decreases, and thus there is a pressure to reduce supply. But if entities are locked into contracts, it becomes very difficult and disruptive to try to reduce supply. Conversely, if there is inflation, then it makes sense for entities to spend money today instead of saving it. If many entities spend instead of save, then liquidity is added to the market, the velocity of transactions increases, demand for products and services increases, and thus there is pressure to increase supply. Increasing supply is much easier than reducing supply because it involves forming new contracts rather than getting out of old ones: it's always easier to make new commitments than to break old commitments. This dichotomy between inflation and deflation leads to effects such as "sticky wages", which is an empirical observation that wages tend not to decrease; if we hypothetically disallow wages from decreasing, then deflation would lead to huge unemployment since workers would have to be fired in order for companies to adjust to the changing market. Because deflation is much more problematic for long-term contracts and obligations than inflation, having a zero inflation target is extremely risky: random fluctuations in the economy would lead to deflation quite frequently, which would disrupt markets considerably. For this reason, even though zero inflation seems like it should be more fair, a positive rate of inflation is better for market stability. How much inflation is ideal, though? That depends on a lot of factors, and there's no best rule of thumb, but we can note that if there is a lot of outstanding debt in the private sector that is becoming difficult to pay back, then a higher rate of inflation may be desirable as it will slowly reduce the value of the debt burden over time. If private debt is not very burdensome, then a lower rate of inflation might be better (as long as it's not too close to zero). Public debt might matter too, but governments with their own currency have a theoretically unlimited credit line (again, people call it "printing money"), so it's unclear to what extent public debt should be taken into account when considering an ideal rate of inflation.
The following are relevant:
http://delong.typepad.com/sdj/2012/10/noah-smiths-sanity-requires-that-he-stop-reading-steve-williamson-foundations-of-monetary-theory-weblogging.html
http://noahpinionblog.blogspot.com/2012/10/money-is-just-little-green-pieces-of.html
http://krugman.blogs.nytimes.com/2012/10/22/things-that-arent-bubbles/
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