If you purchase a callable bond, the issuer has the right to redeem the bond ahead of its maturity date. Callable bonds either come with a call schedule, which outlines specific dates and times the issuer may redeem the bond, or a date after which the issuer can call the bond at any time. These details are delineated at the time you purchase the bond.
An issuer might want to call a bond for the same reason you might want to refinance your mortgage. When interest rates drop, the issuer can take advantage of lower interest rate payments by calling back bonds with high interest rates and issuing new bonds with lower ones. It's possible that only part of the original issue will be called, in which case, the called bonds are chosen by lottery.
If your bond is called, you may have to reinvest your money in a bond paying a lower interest rate, making callable bonds less attractive than noncallable ones. As an incentive to purchase callable bonds, call provisions usually stipulate that an issuer cannot call the bonds until a certain number of years - typically five or ten - have passed after the issue. Alternatively, the issuer may offer to pay a premium above par, leaving you with a potential capital gain.