Class A extinguishers are generally used for combustible substances that we use in our day to day life such as plastics, paper, wood etc. Class B extinguishers are more to do with liquids that are easily flammable, like kerosene, oil, gasoline etc.
Class C extinguishers are related to electrical equipment, like wiring, circuits etc. Class D extinguishers you would generally see in chemical laboratory. These are for high powered fires that are cause by combustible metals like potassium, titanium, magnesium etc. Such extinguishers are designed only for these kind of fires, they are not multipurpose like the other extinguishers.
Further, fire extinguishers may also be classified in the following way: Water extinguishers – consisting of air pressurized water (APW). These extinguishers are made only for A class fires. If used on other material like grease it may feed the fire and cause it to become bigger.
Dry Chemical Extinguishers – they can be used for Class A, B and C fires. There are two types of Dry Chemical extinguishers, BC (sodium bicarbonate) and ABC (monoammonium phosphate). Of the two, ABC is the multipurpose one.
Carbon Dioxide (CO2) extinguishers are mostly used for fires that come under Class B and Class C. These contain CO2 which is under high pressure. They are better than the dry chemical extinguishers in that they don't leave a dangerous residue.