Jan z jani is a phrase in Polish that means "John from John's" in English. Imagine you have a group of friends named John, and one of them is named John Johnson. When you want to talk about him, you might say "John from John's" to help people know exactly which John you mean.
It's kind of like if you go to a school and there are a bunch of people with the same first name, like Emily. To help distinguish between them, you might say "Emily with the curly hair" or "Emily from Mr. Smith's class". That way, everyone knows exactly which Emily you're talking about.
So Jan z jani is just a way of being really specific about which person named John you're talking about. It's a helpful phrase to use when there might be confusion about who exactly you mean.