The words 'fire' and 'burning' are more or less synonymous with 'combustion', and should probably be allowed if asking this question in a quiz.
In order to produce combustion, you need a fuel (such as wood or petrol) and an oxidant (most commonly atmospheric oxygen). To start it, you need heat (produced, for example, by the friction of a match head against sandpaper). Once started, combustion becomes self–sustaining as it produces its own heat.
The heat (and light) produced by combustion results from the energy released by the conversion of the weak double bond in molecular oxygen (O2) to the stronger bonds in the combustion products (carbon dioxide and water).
Rusting and digestion are examples of similar processes (essentially involving the oxidation of a material) but are clearly much less rapid.
© Haydn Thompson 2017