A reverse convertible is a bond that can be exchanged for shares at the option of the issuer. This contrasts with a convertible bond that can be exchanged for shares at the option of the holder. A convertible give the holder an embedded call option, whereas a reverse convertible give the issuer a put option.
This is usually expressed as the conversion being triggered by the share price falling below a certain percentage of the initial nominal level, but the effect is the same as an embedded option. It is common for the exchange to be triggered by a breach of that level, making the embedded option a knock-in barrier call option.
Another common variant are reverse convertibles linked to an index level rather than an individual equity.
The issuer of the reverse convertible is usually not the issuer of the the shares it is linked to. Reverse convertibles are usually created by investment banks, and the effect of the transaction is to buy a bond issued by the bank, while also selling (or rather writing) an option to buy shares at the time the bond matures.
Reverse convertibles usually offer high rates of interest, but the potential upside is limited to the interest. The best possible outcome (for the holder) is getting both the interest and the principal. However the downside is far greater: if the share price falls, then the issuer will issue repay the principal in shares. As the number of shares is calculated at a rate fixed when the reverse convertible is issued (i.e. the put has a fixed exercise price), the potential loss is is large as the possible fall in the share price.
In other words, the risks of reverse convertibles are the risk of holding equities, whereas the potential gain is limited.
Convertibles exist for a reason. They resolve an agency issue. What similarly useful function reverse convertibles perform is not clear, although they clearly do appeal to some investors.