A federal republic is like a big group of friends that live in a big house together. Each friend has their own room and things inside that room. But, they all share the same house and have to follow some rules so everyone can live together peacefully.
In a federal republic, there are different groups of people - like states or regions - who each have their own leaders and governments. These leaders and governments make some decisions for the people who live in their group, like what they can do and what they can't do. But, they all also work together to make other important decisions that affect everyone, like making sure there's enough food or water for everyone, or figuring out how to keep everyone safe.
So just like the friends in the house, the different groups in a federal republic have their own things going on, but they work together to make sure everyone is happy and safe.