Okay kiddo, so rabbinic authority is like when a grown-up who is really important and knows a lot about the Jewish religion tells you what to do. This grown-up is called a rabbi. They are a bit like a teacher or boss, but for things related to Jewish beliefs and customs. They have studied a lot and know what is allowed and what is not allowed according to Jewish law.
When someone follows the rules that the rabbi teaches, they are said to have followed "rabbinic authority." It means they are doing the right thing according to the Jewish religion. But sometimes people might not agree with what the rabbi says, and that's okay, they can ask other rabbis for their opinion or try to understand the reasoning behind it.
Rabbinic authority is important because it helps people understand how to be a good Jew and follow the rules of the religion. But it's okay to question things or ask for advice from different rabbis too.