Local autonomy law is a set of rules that allow people in a particular area to make decisions for themselves without having to always ask the government in charge of the entire country or state. It's like if you and your friends were playing a game and you all agreed on the rules together. You wouldn't need to ask your parents or a teacher to tell you what to do because you all made the rules together.
This law is important because it gives people who live in a certain area the power to make decisions that are right for them. For example, if people in a town decide that they want to build a new park, they can use the local autonomy law to make that happen. The people in the town won't have to ask the government in the state or country if they can build the park.
Another example would be if people in a village decided that they want to start a recycling program. They can use the local autonomy law to do that. They won't have to ask the government in the state or country if they can start the program.
Overall, the local autonomy law gives people in a certain area more control over their own lives. It's like having a little bit of power over your own world.