Explanatory power is like telling a story. Imagine that you have a toy car and it stops working. You want to know why it stopped working, so you ask your parents or teacher for help.
If they just say "it's broken", that's not very explanatory. But if they say "the battery ran out of power", that's a better explanation because it tells you why the car stopped working.
In science and other fields, explanatory power is about how well an explanation fits the facts that we know. Just like with the toy car, if someone gives an explanation that fits well with what we observe and can be tested, it has more explanatory power.
For example, if scientists want to explain why a volcano erupts, they might come up with different explanations. One explanation might be that the pressure inside the volcano gets too high and that causes an explosion. Another explanation might be that a dragon living inside the volcano gets angry and starts spitting fire.
The first explanation has more explanatory power because it fits better with what we know about how volcanoes work. We know that pressure builds up and can cause explosions, and we don't have any evidence of dragons living inside volcanoes.
In other words, an explanation with more explanatory power is like a better answer to a question. It helps us understand things more clearly and helps us make predictions about what might happen in the future.