Lighter fluids typically contain butane, naphtha or kerosene; naphtha is itself a mixture of hydrocarbons, and some lighter fluids may contain propane as well. The product details or material safety data sheet for a given brand will generally specify which of these ingredients it contains.
All of the compounds in lighter fluid are hydrocarbons derived from crude oil or other fossil fuels. In a sense, then, the energy stored in the chemical bonds in lighter fluid is actually solar energy stored in chemical form by plants many millions of years ago.
Since the carbon-oxygen bonds in carbon dioxide and hydrogen-oxygen bonds in water have lower energy and are more stable than the bonds in the hydrocarbon molecule, when the hydrocarbons in lighter fluid are oxidized energy is released as heat and light. This reaction is spontaneous but has an activation energy barrier, meaning there's a certain amount of energy you have to put in to kick-start the reaction.