This is a unit for measuring energy and it is how your energy retailer bills you. A kW/h is one kilowatt of power measured or used over an hour. For example, if you have an air conditioner that uses 3kW of power, it will use 3kW/h of power every hour. If you are billed 25 cents per kW/h by your energy retail, it will cost you 75 cents every hour to run the air conditioner.
Similarly a 2kW solar system will generate 2kW/h of power for every hour that it is outputting power at full capacity. If on a sunny day in summer it works at full capacity for 4 hours and you use all of this power in the home, you will save $2.00 on your power bill (2kW x 4 hours x 25 cents).