Currencies are floating, the trade is a mutual contract to do an exchange of security (in this case X amount of some pair) There is no central place which specifies what some currency costs - the price is just what it is, what the counterparties are willing to agree. This is possible because markets are efficient (in theory).

you might want to read this site The Skinny on Forex | Pre-School: Forex Basics | Learn Forex Trading and this Currency Pair