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The Fed rate is basically the rate that banks are charged for overnight loans of federal reserve money, which they use in order to prevent an overdraft, should many people take cash out overnight. The Fed is basically giving away cash to banks at no charge, to prevent them from finding themselves overdrafted (and then crashing and burning like everyone else does when they overdraft). They're basically a shortcut to funds that work faster than deposits (which need to clear) or interest on deposits (which needs to accrue), and they allow a bank to have more lending power immediately.
Since the Fed controls these funds (banks that draw on them are required to keep a certain amount of reserve funds in the Federal Reserve, from which all this borrowing takes place, rather than direct institution-to-institution loaning), anyway, there's no danger that the lenders will freak out over federal reserve funds being used and prevent the loan from happening (well, they might freak out, they can't do anything about it).
In some weird, reverse way, lowering the Fed Rate actually increases supply, as the Fed pretty much loans indiscriminately and the lower rate means that more banks can afford these loans. It all sort of comes out of a single pool of money that's already there, so the supply won't increase even if it's more attractive for banks to do more loaning.
At least, such is my understanding of how it works. I couldn't honestly tell you if it's actually a good idea or not.