Hi David,
Every training plan has scheduled rest days each week designed specifically to allow your body to reset itself so it's ready to take on the upcoming week of training. A week of training takes its toll on the body and everything from your tissues, to your mind and central nervous system needs a brief period to recuperate.
Your main goal on a rest day is to relax so your body can recover. Every body has a different recovery cycle, therefore rest days will look different for many runners. One direction to go is to do absolutely nothing (per your request! lol). For some, a week of training will be totally exhausting and will lead to a rest day lounging around or taking a stroll in the park and not much else.
Other runners will still have the urge to do something on their rest day. So if desired, this day can be spent participating in any number of holistic or active recovery treatments. Here is a list of a few:
-Flexibility routine
-Acupuncture
-Yoga
-Sauna
-Massage
-Physical therapy
-Meditation
At the end of the day, it is entirely up to the individual runner. If you're completely out of energy - take it easy, you need to. If you feel like doing something - do it but, again, take it easy, it is supposed to be a rest day afterall.
The key to finding the right solution is to learn to listen to yourself, your body. It will get easier over time and with more practice. I hope this helps!
Let us know if you have further question!