There are quite literally markets where money is bought and traded, people literally just saying "I'll give you X of this currency for Y of that currency." But taking an average of these markets, you can determine the relative value of any currency to another at any given time.
Mister_Silverback t1_j5kg9kc wrote
Reply to Eli5: How do we measure whether the US dollar is rising or falling? by SoshiLuver
There are quite literally markets where money is bought and traded, people literally just saying "I'll give you X of this currency for Y of that currency." But taking an average of these markets, you can determine the relative value of any currency to another at any given time.