A bearer bond is a financial instrument that has been illegal in the United States for some time (primarily because it allows anonymous ownership and transfer of wealth, and thusly makes money laundering and tax evasion much easier).
The way the bonds work is still pretty much the same as normal bonds: The person investing in the bonds (the lender) pays some money to the issuing institution (the borrower) and receives some sort of tamper-resistant receipts along with a promise that the investor may redeem those receipts at a later date for the value of the principal plus some agreed upon sum in interest.
The difference between bearer bonds and normal bonds is the following: With normal bonds, the issuer keeps a record of who invested what, and the paper you get is just for your own records, the official record of ownership is kept by the issuer (and a copy is sent to the government so they can tax your profits from the investment). With bearer bonds whoever shows up at the end of the term with the paper bonds walks away with cash. There is no central record of ownership, and therefore it's hard to tax, account for, or trace that sort of transaction.