Complete combustion of a hydrocarbon fuel happens when there is a good supply of air. Carbon and hydrogen atoms in the fuel react with oxygen in an exothermic reaction.
In complete combustion, the maximum amount of energy is given out as its only products are carbon dioxide and water.
Complete combustion:
oxygen + hydrocarbon --> carbon dioxide + water
E.g.
Incomplete combustion happens when the supply of air or oxygen is poor.
During incomplete combustion, water is produced, but carbon monoxide and carbon are produced. Less energy is released than during complete combustion.
In a Bunsen Burner, incomplete combustion occurs when the air hole is closed.