Fire Needs Three Things
Place a burning candle under a glass jar, and the flame soon weakens and goes out. The candle has not suddenly become non-flammable, so something else has changed.
Fire can continue only while the conditions needed for combustion remain in place. Change one of those conditions enough, and the flame can no longer sustain itself.

The Three Ingredients Fire Needs

The traditional fire triangle describes three things needed for combustion: fuel, an oxidizer, and sufficient heat to initiate and sustain the reaction. In most everyday fires, oxygen in the surrounding air acts as the oxidizer.
Wood can provide the fuel, while a match supplies enough initial heat to begin the burning process. Remove enough heat, separate the fuel, or reduce the oxygen supply sufficiently, and sustained combustion stops.
That is why a candle covered by a jar eventually goes out. As combustion continues, oxygen becomes less available while combustion products accumulate, until conditions can no longer support the flame.

Why You Need Enough Heat

A fuel does not begin flaming simply because oxygen is present. It must first receive sufficient heat for the chemical reactions of combustion to proceed rapidly enough to sustain a flame.
For materials such as wood, heating also causes decomposition, releasing combustible gases. Much of what you see burning above a piece of wood is actually a mixture of these gases reacting with oxygen.
There is no single ignition temperature that perfectly describes materials such as "paper" or "wood" in every situation. Ignition depends on factors including composition, thickness, moisture, airflow, heat source, and the duration of heating.

Oxygen Does the Quiet Work

Oxygen is not just background air. In most familiar fires, it is one of the reactants involved in combustion. Fuel reacts with oxygen through a series of chemical reactions that release energy as heat and often as visible light.
Reduce the oxygen supply enough, and the flame can no longer sustain itself. A fire blanket can help extinguish a small, appropriate fire by covering it and restricting the supply of fresh air.
The opposite can happen when blowing gently on glowing embers. Moving air can supply additional oxygen and remove some combustion products, helping the remaining fuel burn more vigorously.

The Chain Reaction Keeps It Going

Once combustion begins, the heat it releases can keep heating nearby fuel and sustaining further chemical reactions. This continuing process adds a fourth element to the fire triangle, creating what is known as the fire tetrahedron.
The fourth element is the chemical chain reaction that allows combustion to continue. Some extinguishing agents can interfere directly with these reactions, while others work mainly by cooling the fuel or by reducing the available oxygen.
Carbon dioxide extinguishers, for example, work primarily by reducing the concentration of oxygen around the fire. They provide some cooling as the gas expands, but cooling is not their main extinguishing mechanism.

Everyday Proof in Your Kitchen

You have probably seen these principles without naming them. Covering a small cooking fire with an appropriate lid can restrict its oxygen supply, while turning off the heat removes an important source of energy.
Damp wood is harder to ignite partly because energy must first heat and evaporate the water it contains. That leaves less energy available to heat the wood and produce the combustible gases needed for sustained flaming.
A campfire also weakens as its available fuel is consumed and the remaining material loses heat faster than combustion can replace it. In each case, changing one or more conditions can bring sustained burning to an end.
The fire triangle turns an ordinary flame into a simple chemistry lesson. Fuel provides material to react, an oxidizer allows combustion to proceed, and sufficient heat keeps the process going. Remove enough of any one, and a flame that seemed self-sustaining can quickly disappear.