Sure, money needs to be portable, durable and counterfeit-proof. But more importantly money should be a:
Unit of Account
Store of Value
Medium of Exchange
Here's a little more detail from Charles Wheelan's insightful and entertaining book Naked Money:
All money—from dollars to pouches of mackerel—should ideally serve three purposes. First, money serves as a unit of account. […] Even as physical money disappears, we will always need some unit of account for pricing transactions. […] Second, money is a store of value. [...] Money needs to be scarce in a predictable way. […] Finally, money is used as a medium of exchange. […] Money need not have intrinsic value in order to be valuable; it need only facilitate exchange.
Money is a way to keep score and evaluate the relative worth of goods and services. Hence the concept of the unit of account:
Prison inmates in the United States are not allowed to possess cash. […] As has been the case throughout history, [informal] commerce becomes easier when there is informal agreement on a single unit of account, such as cigarettes in prisoner-of-war camps during World War II. The item that has emerged as the gold standard for trade in American prisons since the federal smoking ban in 2004 is the pouch of mackerel, or “the mack.” […] Curiously, mackerel has little appeal outside of prison, even at discount retailers. […] Unlike the dollar or the won, the mackerel does have some intrinsic value. You can always eat it.
Source: Charles Wheelan. Naked Money: A Revealing Look at what it is and why it Matters. WW Norton & Company, 2016. [B046]
Here's a example illustrating the idea of the 'store of value':
Residents [on the Pacific Island] of Yap use money called “fei” that consists of large stone wheels shaped liked coins that can reach up to 12 feet in diameter. These fei have many of the optimal characteristics of money. They are difficult to counterfeit and they do not decay. While the fei are not portable, they are stored in the equivalent of banks and do not get moved very frequently. The fei can change ownership without being physically moved. Because the society is sufficiently small, everyone knows who owns which fei, and consequently there is no risk of theft. Many years ago one of the fei was washed away during a storm. The people of Yap faced a choice. Should the person who owned the money be liable? If so, that person would suffer, but so would the whole society. […] The residents of Yap decided that the lost fei should still be credited to its owner. So while the actual fei remained lost, all the residents simply acted as if it were still on the island. They kept track of who owned the fei and—many years later—this virtual fei still existed in everyone’s mind and was used in transactions. The story of stone money on the island of Yap illustrates the problem with any tangible currency.
Source: Terry Burnham. Mean markets and lizard brains: How to profit from the new science of irrationality. John Wiley & Sons, 2008. [B131]
Next, consider the importance of using money as a medium of exchange (which ties into the now-retired 'standard of value for deferred payment' function):
Say that you have ten fifty-pound bags of rice in your basement. You would prefer not to carry them around while conducting commerce. So you create ten elegant paper certificates [where] anyone […] can come and claim a bag of rice from the basement anytime. You have now created paper money, albeit paper money backed by a commodity (bags of rice). […] Here is the irony: as long as the people using the rice certificates are confident they can redeem them at any time, most will feel no urgency to do so. But it’s also true that if there is even a whiff of doubt about the value of those rice certificates—whether it is justified or not—you are going to have a mob of certificate-wielding people banging on your door and demanding rice.
Source: Charles Wheelan. Naked Money: A Revealing Look at what it is and why it Matters. WW Norton & Company, 2016. [B046]
Barter was once used as a medium of exchange. However, this type of economic system is greatly inefficient because it requires a so-called 'double coincidence' to take place:
Before the invention of money, all human societies used barter. […] The need for simultaneous exchange in barter societies places a serious damper on economic activity. Consequently, barter economies are less productive than societies that use money.
Source: Terry Burnham. Mean markets and lizard brains: How to profit from the new science of irrationality. John Wiley & Sons, 2008. [B131]
By most modern definitions, there are only 3 functions of money today, which makes this couplet a bit obsolete:
Money's a matter of functions four,
A Medium, a Measure, a Standard, a Store.
Source: https://en.wikipedia.org/wiki/Money#Functions (Milnes1919)
Note: The function of money that was dropped from the list was the "standard of deferred payment as a distinguished function" (aka standard of value). It is impossible to have functions #1 to #3 without the fourth, so it was deemed redundant.
Admittedly, there is a ephemeral nature to money:
Money is truly an amazing invention that lubricates economic exchange. [Yet] modern paper money has value only because others perceive it to have value. […] Each accepts them because he is confident others will. The pieces of paper have value because everybody thinks they have value.
Source: Terry Burnham. Mean markets and lizard brains: How to profit from the new science of irrationality. John Wiley & Sons, 2008. [B131]