Why do countries hold foreign exchange reserves?

Trade!

If you wish to trade with the world and have nothing to offer in return that I want, then I want to get paid in the currency of my choice.

Let’s say Country X has various natural resources. It wants to trade with United Kingdom. The UK Government doesn’t want those natural resources. So if Country X wants to buy UK based chainsaws, it needs to pay in a currency the UK is willing to accept. “X-Shillings” (Country X’s default currency) is not acceptable to the UK Government.

But if Country X had US Dollars (because of a trade it did earlier with the United States Government), then these US Dollars can be paid to the UK Government.

Why?

Because the UK Government does a lot of trade with the US Government and can use the Dollars. Both the governments have no use case for X-Shillings.