Complete and incomplete

Most combustion reactions result in products where the element(s) concerned have more bonds to oxygen.

For combustion of elemental hydrogen (H2) or hydrogen-containing compounds such as hydrocarbons, the hydrogen-containing product is H2O.
 H2(g) + O2(g)  2H2O(g)

Carbon forms two different compounds with oxygen. 
Therefore the product arising from elemental carbon (or carbon-containing compounds) depends on the amount of oxygen (O2) available for reaction.

CO2 forms if there are two oxygen atoms (as O2) available for every carbon atom (as shown by the reaction equation).
C(s) + O2(g) CO2(g)

CO2 is said to be the product of complete combustion because it has four bonds from oxygen from carbon (O=C=O).
This is the maximum number of bonds that carbon forms to any atom.

CO forms if there is only one oxygen atom available (as O2) for every carbon.
Because O2 has two oxygen atoms, 2 carbon atoms react as in the equation below.
2C(s) + O2(g) 2CO(g)

CO is a product of incomplete combustion because it has three bonds bonds to oxygen (C≡O) and can further react as shown below to form CO2.
2CO(g) + O2(g) 2CO2(g)