The hardest thing to explain (in my experience) is the difference between instantanous (or an average number) of watts vs “energy usage”. Energy usage implies time … watts over time.
Part of that is “easy”: a 1,000W ( 1kW) space heater on for 1 hour uses the same amount of energy (in that one hour) as if you had a 100W lightbulb on for 10 hours straight.
One way of intuiting what energy is is to think of yourself climbing lots of stairs. Let’s say 1,000. If you take a few hours you’ll be fine and not too sweaty (HOT); if you try and run up them too fast you might expire (OVERHEAT). Either method, you’ll use roughly the same amount of energy (glossing over some metabolic details here, but you get the idea) … it’s just that the faster you go the more watts you need to generate in the moment … either method you’ll have the same barbecue justification.
The hard part is having an intuition for the energy usage of many realworld devices that, these days, are often much more energy efficient than they used to be. e.g. a bulb is more likely to be a 10W LED these days. The other aspect is of course for devices that don’t use a constant amount of energy like a fridge or a washing machine. A fridge is the perfect example of a device that you don’t really need to understand the daily cycle (unless something is wrong) so much as knowing how much energy it uses in a month or a year.
Regarding the solar question:
For arguments sake consider a 10kW (=10,000W) solar system (close enough to yours but easier numbers!) and that your average usage throughout the day was 1kW (=1,000W). That means your daily energy use will be a total of 1kW x 24 hours PER DAY or 24kWhr/day
Physics is physics and energy doesn’t come from nowhere … the solar panels will only generate energy when the sun is shining and so on any given day you will get more or less energy but it will average to something like 20-40kWhours PER DAY depending upon where you are and what the clouds are doing. So you can see that most likely you’ll be generating as much energy as you use … if not more.