Currency Explained Via A Thought Experiment:

Phase 1:
Imagine a young, poor, college student who writes a check for 5 dollars. Will that check bounce? Do you feel as though that check is actually redeemable for the 5 U.S. dollars? The answer is probably "yes" or "most likely."

Now I want you to imagine that same poor college student writing you a check for 50,000 dollars. Would you trust THAT? Would you accept that check in exchange for goods or services knowing full well that you couldn't turn it into a bank and receive dollars? The answer is likely, "no." 

This demonstrates how "reputation" factors into the establishment of an accepted currency. [Bitcoin is created and backed by the market set conversion rate to fiat using exchanges. Bitcoin also has alternative uses such as its blockchain technology and decentralized P2P node system, this is similar to how gold and silver have value in art, industry and fashion as well as currency.]

Phase 2:
Imagine a similar scenario except substitute Bill Gates in place of the poor college student. Would you, just on reputation alone, trust that both small and large checks written in Bill Gates' name would be redeemable for cash? The answer SHOULD be a resounding, "Yes, of course." [Consider Bitcoin as the Bill Gates Checks, at first it was merely cashed for fiat, but its reputation and value grew to the point where liquidity became higher and higher where anyone could buy in and cash out.]

Phase 3:
Say he wrote several 1 dollar checks, several 5 dollar checks, 10 dollar checks, 20, 50, and 100 dollar checks and began distributing them among the population. (So many that you started realizing your friends and family receiving them as well.) Up until this point, everybody has simply been taking their Bill Gates checks to the bank and cashing them in for U.S. dollars. [Liquidity for Bitcoin shot up in the market by an increase in supply and demand, both from speculation and market activity. At this point enough people hold Bitcoin to conduct commerce. Since Bitcoin is easily divisible, anyone can use it to purchase a number of things.]

Phase 4:
After it becomes well established that the Bill Gates checks NEVER bounce, people trust exchanging them directly for services and realize they can save themselves the effort of converting them into U.S. dollars. [At this point Bitcoin can be used to purchase many goods and services that could traditionally be purchased with fiat, although it can also be easily converted to fiat at any time as long as the amount being cashed out is never greater than the amount being cashed in.

Phase 5:
The public starts routinely paying for transactions in their Bill Gates checks, which have become an accepted medium of exchange and therefore a currency. Imagine that the public begins to call them "BG bills." [Bitcoin comes to the point where its USD price begins to become irrelevant, as it is so widely accepted it is routinely used as currency for a wide variety of goods and services and price becomes less volatile. At this point Bitcoin is bought less for speculation and more for actual use.]

Phase 6:
Seeing that this new currency has gained wide spread confidence, Bill Gates opens banks around the country and begins allowing people to create savings accounts to accumulate their BG bills. For the time being, these bills are still redeemable for the, now less popular, U.S. dollars. [Bitcoin to fiat exchanges actually begin to lose some liquidity into fiat because people are willing to hold just Bitcoin alone (legal tender laws would make it mandatory to pay taxes in the native currency still). However fractional reserve banking with Bitcoin is much more difficult as there is no "lender of last resort" or central
bank window controlling interest rates, also banks aren't needed by holders of cryptocurrency and customers would only hold their bitcoin in the most trusted banks for a market set interest rate.]

Phase 7:
Concerns over the redeem-ability of this new currency drastically change. For instance, say Gates had issued roughly 50 Billion Dollars worth of BG bills throughout the world. Being that his fortune was only around 50 Billion to start with, if he continues to issue BG bills, they would no longer all be redeemable for dollars. (since he would lack the ability to exchange them for dollars) Hypothetically, if EVERY individual went to cash said BG bills in at the same time, some of those checks would start to bounce. Luckily, that's not a concern in a world which trusts that BG bills are always valuable. Thus, Bill Gates decides to keep issuing lines of credit to people by lending new bills he merely creates out of thin air - simply by writing bad checks. The currency is beginning to function on its reputation alone. [Luckily for us, Bitcoin is decentralized and does not come from any centralized authority. There is also a supply limit of 20,000,000 coins, therefore this point is mute when applied to crypto. However, Bitcoin does survive based on its reputation as gold and silver does. If Bitcoin were to reach this stage, that means demand for fiat becomes so undesirable that you can no longer liquidly exchange your Bitcoin for fiat currencies large easily.

Phase 8:
The public no longer cares about the U.S. dollar. At this point, the country is running entirely on BG bills. The original 50 billion U.S. dollars that started this experiment is now backing a whopping 5 trillion BG bills. Most of that currency cannot physically be exchanged for dollars anymore. The U.S. government decrees that BG bills are no longer exchangeable for dollars and takes us off "the dollar standard." This mirrors what happened when we left the gold standard and began functioning with a reputation-backed currency. [At this point, Bitcoin or any cryptocurrency could take over fiat by pure reputation alone, finally, a voluntary, decentralized and bank free alternative to manipulative fiat currencies. This can be true for Bitcoin, Litecoin, Ultracoin and any other cryptocurrency that makes it to through these stages. What is important is acceptance, aka reputation.]

Conclusion:
This - in concept - demonstrates how a public can come to accept a currency on reputation alone. Whether that be beneficial or detrimental is hotly debated, but it's where we stand today. Our dollar is backed 100% on the reputation of our government. In the past, it was backed by gold, but gold's value was in turn backed by its own reputation. When it comes down to it, it's all about what people think others will accept. Reputation has a lot to do with making that determination.