Notice that it is because money has the properties outlined in definition number 1, that it is a store of wealth and is therefore valuable, that it can function as a standard of value. In modern society, paper dollars or electronic bits and bytes represent money and a standard or scale of value, but modern money has gotten away from being tied to a commodity having real, intrinsic value. Notice that the idea of a standard of value is quite distinct and differen from the idea of a medium of exchange. Saying that one pig is worth two denarii is quite a useful function of money in its own right, but it is not the same as actually trading the denarii for the pig. I know that it sounds nit picky, but understanding this difference can help us to understand some of the peculiar events that occur when something goes wrong with the economy and the money system.
Money is a medium of exchange.
Merchants need to be able to go into a port where the inhabitants of the country have lots of sheep or wine or oak lumber for sale. They take money out of a chest that isn't any bigger than a corner of the purser's cabin. They trade the money for the cargo, which might fill up the whole ship. Suppose an anxious buyer in Rome wanted some fine horses bred in Cappadocia. Without money, the merchant might have to load a cargo of Roman salt, and trade it for a cargo of North African wheat.