The movie tells us that GMAC extended credit against the purchase of cars and that the cars don't really exist or were already sold. It doesn't tell us more than that. HorusKol suggests that the scam is modeled on an actual crime in which GMAC thought it was financing the purchase of non-GM vehicles. It is also possible that GMAC financed the sale of GM cars to the dealer and should have been paid back when those cars were sold to end-customers, but that Jerry sold the cars and kept the proceeds for himself, submitting false documents to GMAC suggesting that different (or anyway unidentifiable) cars had been sold instead.
Similarly, we are not told why Jerry needed the money. Had he lost it gambling, or was he just living beyond his means, or something else, we don't know.
Amendment: HuffPo quotes Joel Coen as saying “…there was a guy, I believe in the ‘60s or ‘70s, who was gumming up serial numbers for cars and defrauding the General Motors Finance Corporation. There was no kidnapping. There was no murder. It was a guy defrauding the GM Finance Corporation at some point.”
This could be the scam @HorusKol referred to, though Joel Coen doesn't seem to have worried much about the details, and in the manner this crime is portrayed in the movie, they don't matter.