Corruption in local government means that some people in charge in your town or city are doing things they shouldn't be doing, like taking money or favors that they shouldn't be taking. Sometimes these people might break the rules so that they can get what they want, or they might make decisions that benefit them more than they help the people they are supposed to be serving.
It's like when you play a game with your friends, but one friend always cheats so that they can win. It's not fair, and it means that the game isn't as much fun for everyone else.
When people in local government are corrupt, it can have some pretty bad effects. For example, they might not spend money in the right way, so the town or city might not have enough money to fix things that need to be fixed like roads or schools. Or they might give favors to their friends instead of hiring people who are actually qualified for a job.
Sometimes people who are corrupt in local government might not even realize that what they are doing is wrong. They might think that it's okay because they are in charge, but this is not a good excuse. It's important to have people in charge who are honest and fair so that everyone can have a good life in their town or city.
So, in short, corruption in local government means that some people are not playing by the rules and are making things unfair for everyone else. This can have some pretty bad effects, so it's important to have honest and fair people in charge.