Okay kiddo, so an independent agency is like when you're playing with your toys by yourself and you get to make all the rules without anyone else telling you what to do.
In the grown-up world, the government makes rules and regulations for different things like air pollution or safety standards for toys. But sometimes they make an agency that's in charge of making sure those rules are followed.
An independent agency means that this group of people doesn't work for the president or any other big boss. They get to do their jobs on their own without anyone telling them what to do. This way, they can make sure the rules are being followed and keep everyone safe without worrying about getting in trouble from someone higher up.
Independent agencies can do things like investigate crimes or regulate industries to make sure they're doing things the right way. It's like having a special group of people whose only job is to make sure everyone plays by the rules, even if they're not always the most popular.