It's not so useful for when putting it on a plane, since you can't have bags attached to it when it goes to be stored.
But if you're pulling the suitcase through town, then you can use it to clip the handles of your other bags and items, so that you're pulling all your bags in one place, rather than pulling a suitcase and holding on to a carry on and other items.
It's just to make travel easier by saving you from holding lots of things.