Puffiness is a state of being soft and round, like the puffiness of an inflatable snowman in your yard or the puffiness of the big, fluffy clouds in the sky.
The puffiness of your swollen eyes may make it impossible to hide the fact that you've been crying during a sappy movie. And the puffiness of your prom dress might make it hard to dance anywhere near your date. The condition of being puffy is what puffiness is all about — although that word was originally used to talk about the weather, as in "The wind is very puffy today!"