Convertible bonds, sometimes called CVs, are issued with the option of converting into a specific number of shares of common stock or preferred stock. While subordinated debentures are the ones most often issued with the conversion feature, any bond issue may include it.
Convertible bonds are often issued instead of stock so that the company doesn't noticeably dilute their outstanding shares in the marketplace. The issuer willingly takes on new debt (which appears negatively on the books), knowing that gradually more and more conversions will be made, so the debt will slowly transform into equity and do so in a way that does not seriously disrupt the stock price.
Convertible bonds are issued with significantly lower interest rates that regular bonds, not only to encourage investors to convert their bonds to stock, but also to compensate for the fact that investors have that option in the first place. For both of these reasons, the issuer benefits from issuing convertible bonds.
But bondholders also benefit: not only will you still receive interest payments when the stock price drops or moves sideways, but when the stock begins to climb you have the option of participating in the joy of capital gains.
The conversion price is fixed at the time of the bond's issue. If the stock price rises well above the conversion price in the markets, then the bond can be sold for a premium in the secondary markets instead of converted. Convertible bond prices in general tend to be much more heavily influenced by the issuer's stock price than by interest rates.