Until very recently, it seemed like nearly everyone believed that monetary policy worked something like this:
The Federal Reserve buys government bonds in the open market and thereby swells bank reserves. The banks then put these reserves to work by lending them out.
Here's Paul Samuelson writing in 1948 (via Paul Krugman) and more or less adopting this way of thinking:
For in the middle of a deep depression just when we want Reserve policy to be most effective, the Member Banks are likely to be timid about buying new investments or making loans. If the Reserve authorities buy government bonds in the open market and thereby swell bank reserves, the banks will not put these funds to work but will simply hold reserves. Result: no 5 for 1, "no nothing," simply a substitution on the bank's balance sheet of idle cash for old government bonds. If banks and the public are quite indifferent between gilt-edged bonds—whose yields are already very low—and idle cash, then the Reserve authorities may not even succeed in bidding up the price of old government bonds; or what is the same thing, in bidding down the interest rate.
That was the basic model: monetary policy is loosened by increasing reserves, which the banks either do or do not "put to work" depending on whether they are feeling timid. Falling interest rates, in this way of thinking, were a by-product of rising reserves.
You can hear a lot of echoes of this line of thinking when people voice concerns that quantitative easing or zero-interest rate targets will rapidly lead to inflation once banks start lending out all of those reserves that they've accumulated.
But that's not how our system works anymore. Quite the opposite really.