Watch people, is it important to put it on the round thing while not in use?

I'm not a watch guy (obviously), but I own 2 and they both come with the oval thing in the box that the watch is originally on, like this:



Should I be using this when not in use or does it even matter? I have one metal band and one leather band. Whenever I'm not wearing I usually just lay them out flat on a dresser, I've never really considered that could be harming them in any way. Any insight, does it matter either way?