Bond issues can contain what is referred to as a call provision, which is a right afforded to the issuing company enabling it to refund the bondholder the par value of his/her bond (perhaps including a small call premium) at the company's discretion. Any and all call provisions applicable to a bond issue will be included in the bond issue's indenture, so be sure you understand the details of the indenture for the bond you are buying.
Most of today's corporate debentures are callable bonds, and about 70% of municipal bonds are callable too - so if you are interested in trading bonds, you should understand how they work.
Call provisions contain several specific rules which apply to the issuer and the bondholder. First, there will generally be a waiting period, starting immediately after the bond issue is offered, during which the company cannot call the bond. This provides the bondholder with a guaranteed length of time he/she will be able to hold the bond. Next, call provisions also specify the price at which the company must buy the bonds back from the bondholders, should it choose to call the issue.
This price is usually set at the bond's par value plus a small premium.
Given the structure of call provisions, firms generally call bonds in situations where interest rates have declined since the bonds were first issued. Why? Because they can then buy back their debt at about par value (which will be lower than market value when interest has fallen) and refinance their debt at lower interest rates. Generally, the investor would prefer to hold on to his/her bond, or at least sell it at the higher market price; unfortunately, once a bond issue is called, the investor must accept the call price specified in the bond's indenture. Primarily for this reason, bond investors generally do not like call provisions. However, most bond issues do contain call provisions because most companies receive strong value from them, as they allow a firm to refinance at lower interest rates when they are available.
Generally, callable bonds offer slightly higher interest rates than non-callable bonds as consideration for this flexibility.
(For further reading, see Call Features: Don't Get Caught Off Guard.)