[meshenna]

Likely it's simply because that's one of the few occasions in modern life when we're not being bombarded with external stimuli. A few minutes of silence and your brain goes: "Right, now's a good time to present this thing I've been working on." Same thing with showers.

[Cshelton]

it also has "occupying" part of your brain with something simple it is used to so it allows you to think of things that would be hard otherwise.

If you simply sat in a chair and starred at a wall, you don't have the same effect as being in the shower, toilet, car, on a walk, etc.

Also for many, simply sitting in a room listening to music can do this as well. It's like your brain needs to distract itself from... itself.