Fire = Heat + Fuel + Oxygen

Fire requires three things - fuel, heat and oxygen (oxidizing agent). A fire can be stopped by removing at least one of them from the context of the fair. Combustion is chemical reaction that feeds more heat to fire and continues it.

Without fuel, the fire can not start or continue. Reducing the heat stops the combustion. Adding water reduces heat in the fire, as water absorbs some energy to convert to vapor. Depriving the oxygen near the fuel controls the fire. Water should not be used for all fires. When there is oil or combustive metals or electricity is near the fire, adding water creates more problems. Covering with blankets, halogen or carbon diode are attempts to reduce the oxygen. Some materials like nitroglycerin acts as both - the fuel and the oxidizing agent.

There is fourth element required for fire to continue. That is chain reaction or continuing the chemical equation. Inert agents like dry sand breaks the chain reaction.

Class A Fires involve wood, paper and fabric. Removing any element extinguishes the fire. 
Class B Fires involve flammable liquids. Inhibiting the chain reaction with halogens suppresses the fire. 
Class C Fires involve flammable gases. Inhibiting the chain reaction suppresses the fire. Class D Fires involve flammable metals. Specialist skills are required to contain the fire. 
Class E Fires involves electrical equipment. Ordinary combustibles control the fire.
Class F Fires cooking oils and fat. They can be suppressed by removing oxygen or water mist.

References
Fire classes
Fire Triangle