What it taught me was to keep my feet closer to the ground when I moved. This may not sound like much of a lesson, but think about how much more unstable you become as your feet get further away from the ground.
Your feet shouldn't really leave the ground when moving in Aikido, whether you're wearing a hakama or not
. We shouldn't lift our feet up ala walking when we move, but should glide across the mat with the sole of the foot maintaining a light contact at all times. The hakama can be a great reminder of this, I once watched a friend being uke for the instructor in class (many years ago), as he stepped forward during his movement his foot went up inside the hakama and his toes caught as he went to plant his foot. It was a great kuzushi movent because it somehow managed to flip him 180 degrees upside down instantly, the only problem was that he dislocated his collar bone when he hit the mat