A convertible bond is a debt security that carries a right to exchange it for a stated number of shares of the issuer's common stock. The SEC describes the wider family this way: "A "convertible security" is a security—usually a bond or a preferred stock—that can be converted into a different security—typically shares of the company's common stock. In most cases, the holder of the convertible determines whether and when to convert. In other cases, the company has the right to determine when the conversion occurs." A convertible bond is the debt member of that family; convertible preferred stock is the equity member, and is covered on the preferred stock page. The tax code uses the term itself: IRC 171(b)(1) closes with the sentence "In no case shall the amount of bond premium on a convertible bond include any amount attributable to the conversion features of the bond."
Until conversion, the instrument behaves as a corporate bond: it pays a fixed coupon, it is repaid at face value if it reaches maturity unconverted, and its holder is a creditor rather than an owner. What the conversion right adds is a claim on the stock's appreciation, and what it costs is the price the market charges for that claim, which usually shows up as a coupon lower than the same company's plain bond would pay.