As above... Surely it must go somewhere?
My child asked me this question and it was a difficult one to answer.
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Light travels at 300,000,000 meters per second. There is a very small period of time after switching it off where there still are photons from the bulb in the room. But these get absorbed/scattered by the wall and thus you don't see them. This what happens to all of the light that came out of the bulb significantly before you turned it off as well -- the photons (or EM radiation, take your pick) are no longer present in the room in their initial form. When the light hits the wall, some of it is absorbed, which heats up the wall ever so slightly (just how sunlight can heat things. For that matter, you can warm your hand even with a flashlight if you hold it in place fo a couple of minutes. You can do the same by placing your hand near a lightbulb). This heat dissipates through the wall. Also, some of it is scattered back with a shift in wavelength -- the electromagnetic radiation is still present in the room, but it is no longer visible. It could be radio waves/infrared waves or even ultraviolet waves. It's harmless, though. Eventually, it all leaves the room in the form of heat.
Remember, a light bulb doesn't "contain" light. It contains a filament, which glows when you pass electricity through it. This exactly what happens when you heat a metal -- the electrons get excited and start emitting visible light. Here, you are supplying energy to the bulb (in the form of electricity), and it gets heated, giving off light. For CFL bulbs the system is more complicated, but it still involves the excitation of electrons.
If you want to explain it to your child, you could do the following home experiment.
Explain to your child that this experiment is similar to the light in a room. As I mentioned, the light (water) disappears through the windows (big holes) and is absorbed by things in the room (small holes), like your eyes. In the case of light, the holes don't need to touch the room because the light - unlike the water - bounces around the entire room. It can reach higher places to escape (or be absorbed), while the water cannot.
So when you turn the light switch on, you are effectively turning on a circuit, which has a light bulb (or several of them). What happens is that the current in the circuit then interacts with atoms in the filament and it causes them to heat up. Heat is just energy, so the atoms gain this energy, and they transition to higher energy levels. When these atoms go back down to their normal energy level, the energy is released as light. This is what we see.
So when you turn off the light switch, the light doesn't go anywhere, the current just stops flowing, which means that there is nothing to give the atoms energy so that they can transition between different energy levels.
The light that is in the room at the time you turn off the light is then scattered and absorbedby objects in the room, which is why the room goes dark
This link talks a bit about light bulbs in a simple context