Introduction: "I, Pencil" is an introduction to the economics behind how goods are produced. Read it first:
I, Pencil -
http://www.fee.org/the_freeman/detail/i-pencilNow, this only works when society has good money to use as a medium of exchange.
Good money has 7 key properties:
1. Portable and transferable
It must be convenient and safe for you to bring it along to wherever you want. Other people, including the government, should not be able to stop you from moving your money. Once transferred, the recipient should be able to verify with absolute certainty that they have the amount of money that they think they have. Good money can't be easily counterfeited. When you give me money, you shouldn't be able to take it back without my permission.
2. Divisible
Money must have quick, easy, and reliable divisibility to cater for all types and sizes of transactions. This is why diamonds are not good money.
3. Durable
It must have good durability: it must not decay. If it does, it's not a reliable store of value.
4. Sufficiently rare and scarce
Money must be scarce enough that people can't just easily get more of it from anywhere. Otherwise, it might not have much value at all; or its value might fall over time. This is why US Dollars are not good money: there is a central authority that can create more dollars at any time, thus devaluing all of the existing dollars.
Until 1965, quarters were made of 90% silver and 10% copper. Since 1965, they are mostly copper with some nickel on top to make them look pretty. In 1964, a quarter was worth $0.25. Today, that same quarter is worth $3.59. This roughly approximates the loss of your purchasing power over the past 40 years.
5. Fungible
You can trade or substitute it for equal amounts of the same thing, and it's still worth the same as what you originally had. This is another reason diamonds aren't good to use for money: each diamond is unique, so they can't be substituted easily.
6. Non-consumable
Oil can't be money because it's a consumable commodity. Other than being useful as money, money need not have any other use.
7. Easily identifiable
Money should be easy to detect and difficult to counterfeit. The US Mint goes to great lengths to make dollars hard to copy. When you have some money, you should be able to easily check that it's real.
Here's a comparison of how different things stack up in terms of whether they would make for good money:
http://coin4.me/2012/05/properties-of-good-money-bitcoin/