Bonds which have the right but not the obligation to convert into a specified number of ordinary shares (or other securities) under specified terms and conditions.
This right is an option in favour of the holder / investor.
In return for this additional valuable right, the investor is generally willing to accept a lower rate of interest on the debt.
This saves interest for the issuer / borrower, at the cost of writing the option.
Convertible bonds are also known as Convertibles.