It is extremely important for two reasons a) it affects all other interest rates b) it indicates the confidence financial institutions have in lending to each other. A crucial factor in the 2008 financial crisis was that the Libor went up dramatically. This exposed key financial institutions like Freddie Mae, and Northern Rock which were effectively bankrupt. Because they were considered 'too big to fail', the were partially nationalised by the US & UK authorities.
By September 2008 Lehman Brothers was essentially in the same situation. It had unsustainable debt and no means to borrow the money to stave off bankruptcy. But in this case the authorities did not step in, triggering the financial crisis.
At the height of these turbulent events the Treasury undoubtedly desired a reduction in Libor to help restore stability. Meetings were held between a senior treasury official and the CEO of Barclays. Both agree that an (illegal) fixing of Libor was not requested. But it does appear that some traders arranged for this to happen.
There is an excellent BBC Radio documentary on the financial impact of the recent Libor scandal: Who are the Libor Losers?
What is a debt default?