Why doesn't the light in my ceiling fan work after changing a light bulb?
It is a bit dependant on the exact internals what is the exact cause, but the most likely one is that the system to switch the light on and off uses an electronic element called a Triac. If it can also be dimmed this is very probable even.

It is potentially possible to burn out a Triac by suddenly switching on a load that's a bit over its limit. If the original engineer had foreseen this he may have made a nice circuit that turns on the Triac when the AC voltage curve is at zero, to make sure it doesn't get overloaded. By turning in the lamp you can have accidentally connected it exactly at the highest point in the AC voltage curve, or near it, causing the maximum current to flow very suddenly through a cold lamp. (Cold lamps very shortly require more current to start glowing if it's a filament or even an affordable energy saver lamp).

If this happened the Triac can stay in conduction mode "for ever", requiring repairs by someone who knows what he's doing.

But to be 100% sure some close-and-personal research would be required.