This is a unit for measuring energy and it is how your energy retailer bills you.
A kWh 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 3kWh of power every hour. If you are billed 25 cents per kWh by your energy retail, it will cost you 75 cents every hour to run the air conditioner.
Similarly a 10kW solar system will generate 10kWh 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 $10.00 on your power bill (10kW x 4 hours x 25 cents).