What is the part of the light bulb that glows?

In an incandescent lamp, it is called a filament. It is usually made out of Tungsten. The resistance in the filament causes it to heat up, and then glow.

In a neon lamp it is plasma, which is an ionized gas. In a fluorescent bulb Mercury vapor is ionized to produce UV radiation, that hits the phosphor coating on the outside of the bulb and that glows.