I don’t understand what the specific principle is behind this air conditioner “saving electricity.”

Based on the law of energy conservation, the output is proportional to the input. Saving power is just a mode—either it’s not really useful, or the cooling effect is poor.
What’s weird is that so many people are still watching it.
The only thing I can relate to is that it’s hot right now and everyone needs to turn on the air conditioner—not the topic of how to save electricity.
Also, today’s air conditioners are almost all Grade 1 energy efficiency. Even if you keep them running nonstop, the electricity bill over a month is only about the price of one dinner at Haidilao.
And there’s more: almost all regions have peak and off-peak electricity pricing, so electricity use at night is very cheap.