The Gladstone-Dale relation is a fancy way of saying that the way light bends depends on what it's going through. Imagine you're walking down a street and you see a straw in your glass of juice. It looks bent, right? But when you take the straw out of the glass of juice, you realize it was just an optical illusion. The same thing happens with light.
When light travels through a material, like glass or water, it gets bent. The amount it gets bent depends on the material it's traveling through. The Gladstone-Dale relation tells us that the amount of bending depends on two things: the refractive index of the material (which basically means how much the material slows down the light) and a special number called the density. The denser the material, the more the light gets bent.
So, if you ever see a straw in your juice and it looks bent, just remember that light can play tricks on your eyes, and it's all because of the Gladstone-Dale relation!