A kilowatt hour (kWh) is a measurement of the amount power used in a home, office, or by a specific device.
The unit specifically refers to the amount of power — in thousands of watts — used over the course of an hour.
You could use watt hours or megawatt hours in the same way, depending if you are using an order of magnitude less or more electricity. Kilowatt hour is particularly useful because in the United States energy utilities charged customers based on the number of kilowatt hours they consume.
By way of example, if you have a dishwasher that consumes 500 watts and you run it for two hours, you will have consumed 1 kWh. So this is a measure of energy usage over time, not a continuous or real-time measurement (that would be the 500 watt number).
Kilowatt hours are the best way to measure how expensive an appliance will be to run. If you look up your local electricity price and then the appliances wattage number you can find the running cost with the following formula:
Electricity Price in dollars/kWh x Run Time in Hours x (Appliance watts x 1000)
And, for clarity, watts measures the current power consumption of an appliance with no aspect of time factored in. This useful to knowing how much something will cost to run only if you know how long it will be operating. This means a dishwasher that consumes more power might be more efficient than one that consumers less power if the dishwasher has shorter run cycles.