Wattage and wattage per hour discrepancy Having moved to a new apartment recently, I checked the water heater and the boiler says that it has a 1500W heating unit, but the kWh said 2.5.
Having only an extremely rudimentary in physics and engineering (I'm a very theoretical mathematician), I tried to compute how much kWh a heating unit rated at 1500W would consume if it were on for an hour, and I got 1.5.
Where does the other kWh go?
 A: I'd say that the power rating of 1500 W relates to the heating power of the boiler - in a perfect world, that would also be what the boiler will draw from the electric grid, but since real appliances always have some kind of conversion losses[1] , the power drawn from your socket will be higher than those 1500 W.
If it is plugged into a socket you can use something like a plug power meter to stick that between the socket and the boiler's power plug to see how much power it actually draws and whether the 1500 W relate to the peak heating power or the power draw from the electric grid.
The rating of "2.5 kWh" is something different, as it is a measure of energy, not power. My guess here is that those 2.5 kWh (or 9 MJ) is the energy needed to heat a completely full boiler filled with cold water to the preset temperature. As you pay your electric energy company for the energy (kWh) you use, not the power (W), the 2.5 kWh tell you how costly your hot water at home is.
Since 1 J of energy allows you to heat 1 g of water (equal to 1 ml of water due to its density) by 0.24 °C (or 0.24 K, since the steps are the same), 9 MJ is enough to heat 50 liters (50 kg) of water from 15 °C to 60 °C - which seems like a reasonable ballpark of a household boiler to me.
If you find out how much water fits inside the tank, you can do even more precise calculations.
Now, how to relate the 1500 W with the 9 MJ (2.5 kWh)? If we believe that the 1500 W is used to heat the water without losses, it needs to run 1 hour and 40 minutes to use up 9 MJ of energy, so it takes that time to get the assumed 50 liters to be "ready" as hot water.

[1] NB, it is an interesting thing to think about how you use electric current to heat your water at home when the power plant supplying the electric energy probably burned fuel to generate the current in the first place - why not carry the coals to Newcastle home and heat your water with them?
