The role of money can be encapsulated in the phrase used in the definition: "medium of indirect exchange." This phrase, however, only scratches the surface as to what role money plays. It facilitates a multitude of goods for goods transactions.
It plays a huge role in the lending and borrowing of capital. Instead of having to find someone who will lend you a tractor you can borrow money and by that tractor. Then, instead of returning the tractor, you can just return the money.
International trade would be virtually impossible without money. Imagine Toyota shipping cars to the United States and having an array of goods shipped back to Japan in return. Toyota would have to make a selection of goods that it wish to have shipped. Instead, they can just have money transferred to their account with which they can by the goods they want when they want.
This example of international trade also points out why imposing tariffs or other restrictions on goods simply makes little or no sense. The parties to the exchange believe that what they get is worth more than what they give. Companies that run a perpetual "trade deficit" believe that the products they receive have more value than the money they send to their overseas suppliers. So, where's the deficit?
I will expand on these concepts in the future.