The phenomenon due which the bulb gives us light through illumination is called "black body radiation", in the visible spectrum range.
An electric bulb contains an electrical filament (thin) in the center. It is usually made of Nichrome (Nickel and Chromium) alloy. It is a hard substance and has very high melting point above 2500 Deg Centigrade.
Radiation from Filament:
When the electric bulb is switched on, electricity passes through it. The alloy nichrome has a very high resistance and so there is a lot of heat generated from it. As it is getting heated, it emits energy. It is called black body radiation. The temperature of the filament reaches up to 1800 deg Centigrade. At this temperature, the alloy emits radiation waves in the visible spectrum (violet to red). So we get bright (white or colored) light.
At this temperature air will ignite (because of Oxygen, Hydrogen, Nitrogen etc). So inside the bulb, a neutral gas like Neon is filled.
Filament from gas :
Often there are gases like sodium vapour, Xenon gas, halogens (chlorine, bromine), mercury vapour are filled in the bulb. They also emit colorful light rays at high temperatures. The electrons in the gas change energy states, and hence, energetic photons are emitted in the visible electromagnetic wave spectrum. These are beautiful, and spread uniform light