Not much if you’re just sitting around.
But if you walk and run a lot, your feet will get a little wider and a lot stronger. The skin on your soles will become very tough, allowing you to walk on a lot of surfaces without injuries.
The muscles in your legs and feet will be stronger, supporting you and preventing sprained ankles. Your circulation will get better so you can walk in snow with no problem. (That also requires generally improving your constitution: It takes a strong heart to pump warm blood all the way to your toetips and prevent frostbite!)
You will develop a habit of watching the ground ahead, so you will subconsciously avoid stepping on anything unpleasant or dangerous.
You might get hard and cracking skin (but that can be fixed with skin care). But it doesn’t have to be bad, this is one of my feet in the middle of a long barefoot hike:
edit, I’m impressed of the number of upvotes. Let me just add that the more you walk barefoot, the easier it gets, not only physically (what used to hurt isn’t that bad any more) but also emotionally (you will forget the fear of what people may think).