Combustion (burning of fuel) can be classified into two: complete and incomplete.
Combustion of the fuel will be complete when there is sufficient quantity of oxygen for the fuel to burn. These results in a blue flame and the heat generated will be maximum. Combustion is termed incomplete when the oxygen supply is insufficient. This results in a yellow flame. As a result, the heat produced is lesser than the maximum obtainable from the fuel.
In the case of a candle flame, as one can see, there are three distinct zones. The hottest zone surrounding the wick is blue in colour. A zone of unburnt volatile fuel forms the centre of the flame. The yellow luminous zone which is responsible for illuminating the room forms a major portion of the flame. This zone contains hot carbon particles which get heated by hotter zone below. They emit light due to incandescence. As they move out of the flame and escape into the air, they get oxidized and cooled. The process continues as more fuel is burnt.
In the case of LPG (liquefied petroleum gas, which is mostly propane and a little butane), the aim is to get the maximum heat energy from the fuel so that the cooking time is reduced and fuel conserved. Hence the incoming gas is mixed with sufficient quantities of air in the burner and then burnt to give a blue flame.
It is known that propane needs about 25 times its volume for complete combustion. Hence by designing the pinhole (which lets the gas into the burner) suitably, the flow of gas is controlled and ratio of gas and air is maintained. As there is no incandescent zone the flame does not illuminate the room. But, sometimes we see that dust and rust block the holes preventing free flow of air. This results in a yellow flame which illuminates the room just like the candle flame.
Also in the case of LPG stoves, as all the fuel that is injected is burnt fully, the heat generated is more and the cooking time is reduced.