This is both the gasoline and the oil for the modern economic engine, and if you and I didn't go into debt and the banks didn't lend more than they have in deposits, the engine would seize up and our entire economy would come to a screeching halt.
But in exactly the same way that you or I might be in trouble if we borrowed a lot more money than we have stashed away in a bank account somewhere, a bank might be in trouble if it lends out a lot more money than its underlying customer deposits or invested capital or otherwise loan-supporting reserves warrant.
Repo 105 was a multiyear scheme by Lehman to defraud the government and its own investors by falsifying the actual amount of loans it had on the books, making Lehman look safer than it actually was.
This is what's called a repurchase agreement, or repo, hence the name Repo 105 (the 105 refers to the 5% overcollateralization that counterparty banks required to lend the cash to Lehman even for a few days – theyknew Lehman was in trouble).
Did I mention that Dick Fuld's nickname was The Gorilla, that he was infamous for controlling everyone and everything at Lehman.