A convertible bond is type of bond that can optionally be converted into shares of the issuing company at some pre-announced ratio. For instance if the bond has a face value of 1000 dollars and the stock is current trading at $10, a particular bond issue might offer 100 shares of the company at some future date, the so-called "maturity date". In general, this is in the company's favour, if the stock price drops they can offer the shares at a lower total value than the face value of the bond. However, if the stock price increases they can instead simply give you your $1000 back.