When things burn, they react with oxygen and produce carbon dioxide and some quantity of energy. This process is known as combustion.
In the case of incandescent bulb, filament (tungsten) gives off light whenever current passes through it. Since the bulb is filled with inert gases (argon or neon), which does not have free electrons or holes to react will prevent the blow off of the filament.
Apart from this, Tungsten has very high melting point and greatest tensile strength. So the incandescent bulb maintain temperature in it's filament without blow off of filament.