In general a currency is a reflection of the state of the economy that it reflects.
The Fed's interest rate is lower than the ECB's. The fed are more committed to pumping and printing more money into the economy than the ECB hence investors are less willing to own or hold dollars.
Scarcity makes a currency more valuable and vice versa.
Also a low interest rate means the return available from holding the currency is lower.
The USA also is up s**** creek without a paddle. Unbelievable level of government and personal debt. World's largest debtor. 70% consumption economy - i.e. no longer a producer and no one there wants to consume anymore. Huge current account deficit. The list goes on.
Europe aint great itself but the joint economies and ECB's general ok economic policies are holding up the Euro for now. Best central bank of an appauling lot so it isnt saying much.
Anyhow all fiat currencies are falling against the only true monetary currency out there - Gold & Silver.