Convertible debt is when a company borrows money from an investor or a group of investors and the intention of both the investors and the company is to convert the debt to equity at some later date. Typically the way the debt will be converted into equity is specified at the time the loan is made.

a convertible bond or convertible note (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value.

In very early stage companies convertible debt is usually only available for small-ish rounds of financing or as a bridge financing mechanism between rounds. The types of investors who are willing to use convertible debt are usually angel investors, strategic investors (maybe a future customer), and very rarely an early stage VC. This can also be a smart mechanism if you're raising money from friends and family as it provides some protection for everyone while still offering a reasonable upside.