Asymptotic safety is a fancy term that means scientists are trying to figure out how to make sure that our math makes sense in all situations.
Imagine you are playing with your toys and you have a toy box. You want to make sure that all your toys stay in the toy box so you don't lose any. But what if you have too many toys and they start falling out of the toy box? That's not good! We need a way to make sure that all our toys stay in the toy box no matter how many we have.
This is kind of like what scientists are doing with math. They want to make sure that all the numbers and formulas they use make sense no matter how big or small they are. They don't want things to start falling out of the equation and messing everything up!
Asymptotic safety helps scientists figure out how to keep all the math "toys" in the "toy box" so they can study things like black holes and the very beginning of the universe without things getting messy. It's like using a really strong toy box that can hold all your toys no matter how many you have.