These two rates serve different purposes. The Fed Funds rate is the rate at which banks earn interest on money held there (so keeping it low encourages banks to not keep it there, raising it does the opposite).

LIBOR (and there are different LIBORs for different currencies and maturities, the main one is USD 3-month) is the rate that banks lend each other on an unsecured basis. Technically, each bank determined their own LIBOR based on how they see the market and what they believe they can borrow at (hence our problems).

The important thing about LIBOR is that many trillions in notional of derivatives use it as a reference, so changing it has very real impact for all market participants (including pension funds, etc.). Even floating rate loans are often based on LIBOR.