When you burn a piece of wood in a campfire, chemical energy is released.
In wood, the energy stored in the bonds of its organic molecules (primarily cellulose and lignin) is released through the process of combustion. During combustion, the chemical bonds in the wood react with oxygen from the air, producing heat and light as byproducts. The heat energy can be felt as warmth from the fire and can be used for cooking or heating.
So to summarize, burning wood primarily involves the conversion of chemical energy to thermal energy (heat) and light.