Why are some materials more flammable than others? Wood and oil are flammable materials, but water isn't. Moreover, flames spread a lot faster in oil than in a piece of paper. What is the reason that it is so?

I also don't know why a small flame can spread out to a very big flame; what is the physical reason for it? I would like to know the molecular reasons in detail what makes fire so powerful.
Firstly, for a material to be flammable it needs to contain something that is oxidisable by air oxygen, typically carbon. This explain why hydrocarbons and other carbon bearing materials typically burn well but minerals, rock, glass, water etc do not. In the latter materials the elements are already in a high Oxidation State and cannot be further oxidised.

For a generic hydrocarbon the oxidation reaction by air oxygen is given by the following reaction equation:

$$\ce{C_nH_{n+2}(g,s,l) +\frac{3n +1}{2}O_2(g)-&gt; nCO_2(g) +\frac{n +2}{2}H_2O(l)}$$

The second major factor that affects flammability is volatility. The more volatile a material is, the more flammable it will be. The hydrocarbons illustrate that well. Methane is the most volatile and flammable of all of them and by the time we get to the solid ones like paraffin wax, flammability has been greatly reduced because these aren't volatile at all.