A polarized capacitor forms the dielectric between the conducting plates electrochemically. Voltage must be applied in one direction only across the conducting plates to form the dielectric insulating film. The applied voltage across the capacitor must always be in a particular direction, and the capacitor is externally marked to indicate the proper voltage polarity. Reversing the applied voltage can cause the insulating film to rapidly fail, and can cause the capacitor to actually explode from rapid production of gas within the shell of the capacitor.
A non-polarized capacitor uses a dielectric material with uniform insulating properties (such as mylar, mica, glass, etc.), and can be installed in a circuit without regard for the polarity of the applied voltage.