Italy here. Usually factories and many offices shut down for at least 2 weeks in August. Essential services obviously stay open.
Some other services may or may not decide to close, like a butcher may decide to close for a few weeks in the summer. Same for some bars/restaurants etc. Not all of them, some of them.
Also there’s a huge difference between where you are. If you live in the industrialized north, then what I described it’s more or less true, but if you live in the south, it’s all completely different. August becomes the busiest period for the tourist-centric south, with bars and restaurants working at maximum capacity, beaches and cities all full of tourists and service workers actually increase in this period.
It’s obviously not 100% all society shuts down, but if you are an American company trying to do business with Europe in August, just keep in mind that lots of stuff will be postponed to September.