For the curious, here is a good recap of the troubles at AIG (American International Group). Basically, AIG is a huge insurance company that in 2008 insured many supposedly safe assets for other financial institutions. When these assets started looking risky (many were housing market related), it became clear that AIG would not be able to make good on all its insurance payouts. Had AIG failed, it would have taken much of our financial system with it. Hence, AIG was "too big to fail".
Falling Giant: A Case Study Of AIG by Gregory Gethard