Why is a burning candle luminous?

A burning candle is luminous because the combustion of the candle's wax produces heat, which vaporizes the wax into gas. This vapor then ignites, creating a flame that emits light as a result of the high temperatures involved. The flame generates light across a spectrum, including visible light, due to the excitation of gas molecules and the production of incandescence. Consequently, the light we see is a combination of thermal radiation from the hot gases and the glowing particles in the flame.