Have you ever seen a straw that bends when you look at it from different angles or through water? The kramers-kronig relation is kind of like that! It helps us understand how light or other kinds of waves bend and change when they go through different materials, like water or air.
The kramers-kronig relation says that if we know how much light or other waves bend and change in one way (like how much they slow down or speed up), we can figure out how much they bend and change in another way (like how much they change direction or intensity). This is really helpful for scientists and engineers who want to study and control how waves behave.
It's kind of like if you have a toy car that can drive forward and turn left or right. You can figure out how much it turns left or right based on how much it drives forward, and vice versa. The kramers-kronig relation is like a rule for figuring out how toys like that work, but for waves instead of toy cars!