Our "What is it?" post entitled "Electric Power" sparked (no pun intended) some nice detective work by Ryan and Phil, and they successfully figured this one out. The device on the wall is an inline water heater. A typical water heater in America (usually in the garage or the attic) will heat water and then store it for use; an inline water heater only heats the water as it passes through the heater. This naturally creates a trade-off: Either you can have volume of water or you can have hotness of water, but not both. And there's another variable you can't see, our large water storage tank out back. The longer that's been in the sun, the hotter the water will be.
So, what do we see in this picture? As I mentioned earlier, there's no shower or bathtub, just a curtain rod. And there's actually not just one water heater, but two; the second one is for the kid's shower. Does all of this look a little weird? It is. Notice the mismatched tiles: colorful on one wall, white on the other. It seems that there used to be only one giant bathroom upstairs, and the owner split it into two bathrooms by simply adding a wall (the white one) down the middle. Hence the weird location for the shower and the two heaters. All in all, it makes for a functional, albeit different, bathroom.
And to answer your thoughts, Phil, there's a water pump in the back yard which pumps it up to the bathroom. It doesn't work by pressure here, like it does in the States.