"A rapid, persistent chemical reaction that releases heat and light, especially the exothermic combination of a combustible substance with oxygen."
--The American Heritage Dictionary, 2nd College Edition

Fire is a chemical process which requires Oxygen, heat and fuel to occur. The omission of any of these three elements will cause the reaction to terminate (or not to begin in the first place). Before I go any further - a chemical process is the process whereby the molecules of a given substance rearrange themselves. As a result of this, energy is either released or absorbed.

The Process that causes fire is called Oxidation. When you strike a match the Oxygen atoms combine with Hydrogen and Carbon to form Water and Carbon dioxide. The equation for this reaction is this:

2H2 + O2 -> 2H2O

Note:If the term Oxidation sounds familiar - it's the same process which causes rust. In the case of Iron rusting the reaction is VERY slow and the heat energy released is therefore VERY low.

The above equation uses the relatively simple example of a burning match. Different materials (fuels) have different Oxidation rates, for example paper and wood burn very quickly (the oxidation rate is very high). The combustion occurs at the point where the generated heat cannot be released faster than it is being created. Each type of fuel also has a different ignition temperature. This is the threshold temperature at which the fuel can rapidly unite with oxygen. Even with a seemingly simple fuel such as methane (CH4), more than 100 individual chemical reactions take place.

If the fuel/oxygen ratio is too high there will not be enough oxygen to allow the fuel to fully oxidize. The results of this can include the formation of carbon monoxide (CO) instead of co2 and a sooty flame. This can be observed as black smoke coming from a car with a too rich mixture (when the mixture is correct all of the fuel is being oxidized and the exhaust is clear).

Flame is the visual signature we can see as the result of fire. For a long time Flame was considered to be one of the elemental components of matter, along with Earth, Air and Water. This is not true. Flame is essentially just a (very) hot gas composed of Oxygen, Nitrogen, Carbon dioxide and water vapour (created by Oxidation - see above).

The reason we see the flame is that some of the heat energy is absorbed by the electrons in the gas. The electrons radiate this energy as light. The common colours for flame (highest temperature to lowest) are: Blue, Yellow, Orange and Red. Below this point the radiation falls into the Infrared - so we can't see it but can still feel it as radiant heat. This low radiation actually comes from the vibration of the molecules rather than the electrons themselves (which have returned totheir lowest energy state).

Flame also has a distinctive shape which you can see when you light a match or candle. This shape is formed by convection currents around the flame which are formed thus:

  1. Oxydiation causes the air around the flame to heat up, becoming lighter than the surrounding air.
  2. The heated air moves upwards (you know that hot air rises right?).
  3. The moving air stretches the flame vertically, resulting in the familiar teardrop-like shape we all know.
Obviously the hotter the fire is the higher the flames will reach as the air is rising more rapidly and takes longer to cool back to ambient temperature.

Sources:
http://www.energyquest.ca.gov
http://www.pbs.org/wgbh/nova/fireworks/fire.html


Note: This information is the result of my research only. If anyone with actual chemistry experience has any corrections/additions please /msg me and I will include them in the w/u. Thanks.