How fire works

If a substance is flammable, heating it to its "ignition temperature" will create a combustion reaction, and the substance "burns"; more specifically "the compound molecules break apart, and the atoms recombine with the oxygen to form water, carbon dioxide and other products."

The light we see produced from fire is created from "the rising carbon atoms (as well as atoms of other material) emit[ting] light."

Source: http://science.howstuffworks.com/fire1.htm