A nanny state is like having a grown-up or a nanny turn your everyday decisions into rules that you have to follow.
Think of it this way - sometimes when you're playing, an adult will tell you not to do something because it's dangerous, like climbing too high or playing with sharp objects. They do this to keep you safe and make sure you don't accidentally hurt yourself.
Similarly, a nanny state is a government or authority figure that puts rules in place to keep their citizens safe, healthy, and to prevent them from making bad decisions. For example, they might make laws about what foods you can eat, or ban certain activities like smoking in public places. They do this to try and make sure that everyone is healthy and safe, just like a nanny would try to keep you safe when you're playing.
However, some people argue that too many rules can take away people's freedom to choose, which makes them upset. They may also argue that not all of the rules are necessary or helpful, like making it illegal to drink alcohol or making it hard to buy certain products.
So, a nanny state is like a grown-up telling you what to do, but when it's a government, it can affect everyone's lives and choices.