Convertible debt is any borrowing that the lender can, or in some cases must, exchange for shares in the borrowing company instead of being repaid in cash. Until conversion it behaves like ordinary debt, paying interest and ranking ahead of shareholders. The most common listed form is the convertible bond, whose entry explains conversion ratios, premiums and pricing in full.
"Convertible debt" is the broader umbrella. It also includes the convertible note used in early-stage start-up funding, which normally converts at a discount at the next priced equity round, as well as privately placed convertible loans and mandatory convertibles that must turn into shares on a set date. A simple agreement for future equity (SAFE) converts in a similar way but is not debt, because it carries no interest or maturity.
In company accounts the term appears as a balance-sheet line, and accounting standards decide whether the conversion feature is shown separately or treated as an embedded derivative. Conversion dilutes existing shareholders.