AIG are a very large insurance firm. One of the things they have insured in the last few years is bank lending based on the sale of mortgages. The idea is that in the event of a bad mortgage, the insurers indemnify the bank against potential losses. Many of those large losses are now being called in and AIG does not, apparently, have the resources to meet them. Unless the US Federal Reserve Board* intervenes, it will go down like Lehman Brothers – except that the business links and obligations AIG has are much wider than those of Lehman. There are more than a few commonplace UK names in the reporting following from The Guardian, the Telegraph. Time magazine has a good overview piece too.
Mind you, if you want a laugh, you can always watch the government(s)
* Effectively, a coalition of major US banks, many of whom may well be in individual financial trouble themselves