An embedded option is an option that is part of another security. It therefore does not trade by itself, but it does affect the value of the security of which forms a part.
Analysing embedded options is essential to valuing securities that contain them. For example, the value of a convertible bond is (by the law of one price) that of an equivalent bond that is not convertible plus that of a call option on a share. The embedded call option is on the issuer's share with a strike price of the maturity value of the bond and an expiry date that is the date on which the bond matures.
More subtly, the value of a bond that is redeemable at the option of the issuer, has an embedded short position in a call option. The holder has effectively written a call option to the issuer. The value of the bond is the value of an equivalent bond that cannot be redeemed early, less the value of a call option over the bond.
Even ordinary shares in a company that has debt may be viewed as options to purchase the company free of debt by paying off the debt. This is not an approach that is often used, but it is theoretically correct.