Burning requires fuel and oxygen. Organic carbon in the fuel is combined with oxygen. This releases carbon dioxide, water, and energy. The reaction can happen without human intervention (for instance in a forest fire) but humans have learned to control the reaction, and release the energy stored in carbon-based fuels.
Whenever something burns much of the carbon it contained is pumped back into the atmosphere as carbon dioxide - for example, in a forest fire, the complex organic carbon compounds that the trees have built up and stored over years are broken down in a matter of hours.