The face value of bonds usually represents the principal or redemption value. Interest payments are expressed as a percentage of face value. Before maturity, the actual value of a bond may be greater or less than face value, depending on the interest rate payable and the perceived risk of default. As bonds approach maturity, actual value approaches face value.
In the case of stock certificates, face value is the par value of the stock. In the case of common stock, par value is largely symbolic. In the case of preferred stock, dividends may be expressed as a percentage of par value.
The face value of a life insurance policy is the death benefit. In the case of so-called "double indemnity" life insurance policies, the beneficiary receives double the face value in case of accidental death.
Face value can be used to refer to the apparent value of something other than a financial instrument, such as a concept or plan. In this context, "face value" refers to the apparent merits of the idea, before the concept or plan has been tested.
Taking someone at face value is assuming another person's suggestion, offer, or proposal is sincere, rather than a bargaining ploy.