Ultimately, it comes down to the inflationary policies of a nation, purchasing power parity and investments into a country.
It is far from a random event, and is a major part of fiat currencies.
Hopefully I can explain it best this way:
The value of one currency versus another takes into consideration what goods and services cost in a country, for its native currency. If the policies of a government are poor, then there are chances that PPP and inflation will become different in respect to other countries' fiat currency.
Ultimately, it comes down to currency transactions between countries. If investors and trade transactions believe that a countries' currency is becoming less worthwhile (due to the printing of more money, or more restrictive rules and regulations on business investments), then the amount of money traded will drop, and the currency will become of less worth.
So in the case of the USD against the EUR, most currency investors believe that the worth of the US dollar (as an extension of inflation and business policies) are going to weaken versus the Eurozone, so they sell off the currency, and buy Euros. That causes swings in the worth of the currency.
Back from the dead, I'm afraid.
