Closed toed shoes are the shoes in which your fore foot is totally closed especially concerning to the toe, if you put on closed toed shoe; that means you are putting on a shoe that is entirely covered.
You are more likely to put on closed toed shoes in factory area, and places where safety precautions are mandatory.
Foot protection is of course needed depending up on your activities, in normal routine nobody likes to put on closed toed shoes, especially if you are talking about summers, then nobody wants to bear that heat, but just think of surrounded by some heavy machinery and equipment that might hurt your feet even if it touches you slightly.
In that case everyone loves closed toed shoes, and they can be life saviors when it comes to save you from sharp objects.
I remember once I saw one of my friends had heavy duty boots, and they had metal toe inside of them, so even if you stand on those shoes or stomp them, it would not hurt the person wearing those shoes, so I asked them why he was putting the them on and he told it is because he had to go to workshop and that was metal work, related to plumbing, so that made quite sense.
And not just this, these shoes are also quite popular to keep your foot safe from animals, if you are working in zoo or something like that.
So make sure to stay protected while working in such areas, this is also proved by University of Missouri, that closed toed shoes are mandatory while dealing with heavy equipment, close contact with wild and large animals, in warehouse, as it is a standard safety precaution, that you must follow.
So always buy yourself quality closed toed shoes when you are going into field work.