One kilowatt is exactly 1,000 watts. It is a plain decimal shift, but the pair is worth stating because it is the boundary between the appliances in a home and the systems that supply them.
About the units
The watt is the SI unit of power, one joule per second, named after James Watt. Power is a rate rather than a quantity: a watt says how fast energy is being used, not how much. That distinction is the one thing worth being careful about here, because watts and watt-hours are constantly confused. A 2,000 W kettle uses energy at a rate of two kilowatts; run for six minutes it consumes 0.2 kilowatt-hours. The kilowatt is the same unit with the prefix kilo, and it is the working unit for anything from a household appliance upwards.
The exact factor
The factor is exactly 1,000. A useful ladder for scale: an LED bulb is 8 W, a laptop 45 W, a refrigerator averages 100 W, a kettle 2,000 W, a domestic electric car charger 7,400 W, a fast charger 150,000 W, and a large wind turbine 5,000,000 W. Household electrical circuits are limited by current rather than power, so a 16 A circuit at 230 V carries at most 3,680 W — which is why two kettles on the same circuit trip the breaker.
Where you meet this conversion
Appliance ratings, electrical installation and solar panel output. Photovoltaic panels are rated in watts peak and arrays in kilowatts, so a 20-panel installation of 400 W each is an 8 kW system. Audio amplifier output, lighting loads and heating elements are all specified in watts while the supply is designed in kilowatts. Any calculation of running cost starts here: multiply the kilowatts by the hours to get kilowatt-hours, then by the price.