How does a light bulb convert from electrical energy into thermal energy?

Using a high-resistance filament. This is the part that lights up in the bulb, it's like a tiny electric heater--it heats up due to the current being forced through it.

The filament in the light bulb is a low resistance.  This produces light and heat emission.  With low voltage or higher resistance (like on the old stove) there is not much light coming out, slightly red, but a lot of heat coming out to cook stuff.  You could actually cook stuff on a light bulb.  The hotter the light bulb, the more light it emits.  This is the black body emission curve.  You can look it up on Wikipedia.

The electrons from the electricity are crossing the filament.  While doing so, there is a resistance and they heat and leave the the filament as photons of various energy.

In an incandescent bulb, there is a very small tungsten filament that has high resistance. When current is forced through it glows white hot. That is the light. It is about 40% efficient. The rest is heat. Wires get hot when current is forced through them against resistance. Resistance is dependent on thinness of a wire, material and length.