With rates negative there, it makes sense for savvy traders to borrow in Euros (and get paid for it), convert those Euros to Dollars at a U.S. bank (which requires that the bank have dollars available), and then lend in Dollars (and get paid for it). With everybody doing this, the banks quickly run out of dollars and accumulate large euro reserves. The accelerated lending at the discount window is needed so that banks can service all the traders looking to exchange euros for dollars.
The natural economic response to the carry trade would be for the euro to weaken and the dollar to strengthen until interest rates equilibrate, but this'd have political implications that are unacceptable: notably, it'd make American goods even more expensive overseas and deepen the trade imbalance, which would cause job losses in manufacturing and other competitive domestic industries, which would sell out Trump's base for Wall Street's interests again. So the respective central banks get locked in a competitive race to the bottom, where the ultra-loose monetary policy in Europe has to carry over to the U.S. because otherwise either exchange rates or interest rates has to move opposite stated government policy.