How is the sun the ultimate energy source for food?

There are chemical reactions that only work in the presence of light. One of these is a rather complex reaction that combines carbon dioxide and water to form such things as simple sugars. To simplify:

12 CO2 + 11 H2O -> C12H22O11 + 12 O2

The reaction uses energy from light. A reverse reaction can be done, and uses the sugar and oxygen to give off energy. This is sort of thing is the basis of life. Notice that in storing energy, we are storing carbon and hydrogen.

The sugars do not last forever, as all carbon atoms have a tendency to break down. Sugars will turn into simple hydrocarbons over time, giving up the oxygen they hold, and taking on such forms as (for example) octane, which is C8H18. During the time the molecules decay, they are sometimes subducted into the earth's crust, forming coal and oil in the process.

So a chemical reaction that was fueled by light eventually causes a build up of underground carbon and oil.