Okay, so imagine there's a group of people called the mafia. They're kind of like a big gang, and they break the rules and hurt people to get what they want.
Now imagine that instead of just being a group of criminals, the mafia gets really powerful and starts controlling things like the government and the police. They make their own rules and do whatever they want, and nobody can stop them because they're in charge.
That's what we mean when we say "mafia state." It's a country where a group of powerful people act like a mafia and control everything, even though it's supposed to be run by a fair government that's supposed to take care of the people. It's really bad because the people who are supposed to protect us are the ones who are hurting us instead.