Maybe there are different types, the one we have in work looks like a small water tank with a heater. You can hear it kick in and boil water now and then too, so I guess it is keeping a reservoir at temperature. I can't see that being cheaper than a kettle for a private household, unless there's someone making cuppas every 5 minutes!
RedByrdz, I think is right on this.
The instant boiling water dispensers retain a relatively small, insulated reservoir at/near boiling point so that the first few centilitres are at the right temperature. They rely on a high power heater which heats the majority of the water 'on demand' as it is drawn through the device.
You will use pretty much the same amount of energy to boil your water whichever technology you use (~0.00116 kWh/kg.K at 20°C). The main difference in economy is the amount of water that is heated but not used.
'Savings' are always dependent on whatever comparison you are making. If the counterfactual is a kettle that is routinely overfilled by multiple people several times a day (e.g. in a shared/work kitchen) then I think they can do reasonably well. There may also be H&S benefits over kettles in a commercial environment. In a low occupancy, domestic setting I suspect they are more of a convenience than an energy saving appliance.
I do not believe instant water boilers can be 50% more efficient in anything other than some highly convoluted and favourable scenario ('energy saving' appliances rarely state in any meaningful way the conditions under which such savings are possible). As the savings are only made at the margins you would need a lot cups of tea before you will realise any savings against the initial outlay.
For reference, a ~Ł1200 cost (excluding installation) would pay for enough electricity (even at 34p/kWh) to bring about 37,000 litres of water from 15°C to 100°C.
