These are handheld fans called uchiwa. They do not fold. They used to be made of bamboo and paper like the green one in the picture. Plastic and paper ones are more common now. Summer scenes, summer patterns, animation or popular characters or advertisements are printed on them. We use them in the car when we first get in and the car is hot (especially in the back seat). We also use them at home.
Someone once said that fanning oneself did not really help. I think it does. I've had a lot of experience over the years. We don't use air conditioning in every room. There are places like on the train where the air is hot and stuffy.