(1) a numeraire: This means that goods and services can be valued easily in one term of measurement, such as dollars. This is instead of valuing 1 t shirt as 3 fish, or 4 shoes, we can value it as $10.
(2) a means of exchange: This means that we can use money to exchange for goods and services instead of barter.
(3) a store of value: This means that we can delay our purchases or save for future spending. If money were denominated in fish, we would have to get a new supply every few days and the store of value would not be very good. If we put $1 under the couch, a year from now it is still worth $1, not spoiled and stinky.
(4) a source of liquidity: Liquidity means that it can be exchanged for goods and services very easily (similar to 2). If we use money to purchase a stock/bond/CD or house, it is no longer liquid, but holding money is an easy way to save money but still be able to use it readily.
Other properties money should have:
(A) Money should be easy to transport and identify
(B) Money should be durable, easily divisible, hard to counterfeit and easy to store.