It's become a joke in my workplace. I'll turn to my boss and say "I had a shower moment this morning. I was thinking about the way that we've built the new code...."
A "shower moment" is when I'm not really paying attention to where my mind is wandering. I'm doing something that occupies my mind enough (but not too much) so that my subconscious can daydream.
These moments are gold.
In the office during the day I'm rushing here, rushing there, trying to beat a deadline, prepare for that next meeting, answer an email, etc. Who's got time to breathe, much less /think/? That nagging little voice that's trying to tell me something never gets a chance.
As an Engineer, I specialise in focusing deeply on a single facet of an application at a time. I build huge architectures of imagination when programming (which is why a single 15 second interruption can be fatal). By necessity, I do my best to make sure my mind doesn't wander off the path to the next challenge. This not only enables me to laser focus on a very small detail, but it also very effectively blocks any 'A-HA' moments. The path is set in stone (until we've conquered the next challenge).
So when I can daydream my subconscious takes the wheel and takes me to places that I wouldn't have gone during the work day. I don't get bogged down in what's known to be possible, what I have to do next, or what anyone else thinks.
It's not strictly tied to when I'm taking a shower...the key is to be bored enough for my mind to wander. I could call this the "doing the dishes" moment or the "walking to the train" moment or even the "boring" moment, but it doesn't have quite the same ring.
Next time you find yourself standing in a queue at a Starbucks, waiting for a meeting to begin, sitting in a waiting room for your next dental exam or even in a shower, don't pull out a phone or a tablet (especially in a shower).
Just relax and let your subconscious take you where it may. Bring a way to take notes, and see what that little voice is telling you.