A debenture is an unsecured debt. It is simply a promise by the borrower to repay the lender. A debenture will mature on a specific day and state an interest rate. This rate may be fixed, or tied to some sort of index, such as the London Interbank Offered Rate or the Federal Funds rate.
Most corporate bonds are debentures. The rate of interest a corporation will pay on its bonds is a function of the market's perceived risk of the corporation being unable to repay the debt. Debentures may also be issued by privately held corporations.