My answer on Quora:

Let’s define a world currency as a widely used currency for both international transactions and official reserves. An alternative interpretation would be a single currency for the whole world (see here for more on that).

Direct benefits include very little exchange rate risk in international transactions, importing goods using your own currency (limits/eliminates balance of payments crises), world commodities priced in your currency, and greater seignioragebenefits (profits from the value of the currency being greater than cost to print).

Perhaps more importantly is that having a “world currency” tends to be an outcome of having a stable government, a large economy, a deep and liquid financial system, and far reaching influence around the world.

The US dollar’s role in the world economy has often been said to give the United States an exorbitant privilege:

• The dollar’s international role: An “exorbitant privilege”? (wonkish)
• Imagining the Dollar Without Its Privilege