A debenture is simply a debt instrument that is issued by an entity (typically a business firm or a government) and that is not backed by any sort of collateral. The only security for the person who lends money (buys the debenture) in this case is the faith that person has in the entity that is issuing the debt.
A mortgage, then, is not a debenture. A mortgage is typically secured by the home or the land that it is being used to buy. Government debt, on the other hand, is a debenture. When you buy a government bond, you do not get the right to any collateral in case of a default. You simply have faith that the government will repay and, on that basis, you loan the money (buy the bond).
In simple words, a debenture is a medium to long-term debt format that is used by large companies to borrow money. They enable investors to obtain double Benefits of Adequate Security and Good Returns. Generally, private sectors issue this kind of debt instruments.