Definitely: A tragedy waiting to happen!
Yup: An attempt for create some kind of shower/spa thingy.
Nope: Is that one of those shower-head water filter devices?
Possible: Looks like an attempt to get some luxury into a somewhat sad "shower arrangement". (If by luxury you mean an assured supply of hot showers!)
Yes: An in-line shower heater.
Yes: An electrical water heated shower-head, made in Brazil.
No: An automatic wash and body wax. (Editor's note: Entirely more fun when done to you by a willing particpant).
True: A double-headed shower thingy.... used when you have more than one occupant in the shower

Could be: Looks like those posting here need a cold shower! :-(This thing is to AVOID cold showers.)
Good point: If that's a shower water heater how much would it hold? (It holds nearly nothing. It heats the water instantaneously as it passes through. Compare to a heating element in a Bosch DW.
Here is why I was HORRIFIED to see this instantaneous shower-head water heater during a building inspection:
1)Electricty and water don't mix. Period end-of-story.
2) That yellow wire is for indoor(dry) areas only. Waterproof wire is sheathed in gray. Plastic sheathed wire may still be illegal in apartment buidlngs in NYC. It was only recently approved for use in very limited circumstances.
3) The wires are joined in mid-air, open to the elements and water. (A waterproof junction-box woould be nice, n'est ce pas?
4) Out of view is ONE circuit breaker protecting the circuit. If that sucker is 220v (and it would make sense that it needs to be) there should be TWO; on for each hot leg.
5) There is no GFCI (RCD) protecting the line and from frying the bather(s).
I have seen instantaneous showers in Brit publications. At least the wire in thier version come in from the back and are sealed. This however.. OH LA LA LA LA. No ways Jose!
This was a very poor neighborhood and is in an ancient buildng. It appears the tenant wanted to have hot water at all times. In NYC the landlord provides heat and hot water. IIRC this building had the intantaneous tankless water heating coil (located in the boiler) replaced. So my guess is the tenants had intermittent hot water the last month or so.
I'm not sure ths instantaneous heater would even be efective given NYC water temperatures in the winter. Esp. if operated on 110v.
Does anyone have a link to other instantaeous shower water heaters? The brazilian site is of particular iterest.
Here is a Brit instantaneous shower:
http://www.plumbingpages.com/featurepages/SElectric.cfm