It took me a while to recognize the need for it. (I am a slow learner, what can I say...)
When I started training for 10K, 10 miler, Half Marathon, it became obvious that those who write the training manuals do have an idea what they are talking about:)
I don't necessarily observe rest day on the assigned day - I play it by ear. Whenever it becomes too difficult to make it to the gym or if I feel overwhelmed, that becomes my day of rest.
Today was a day or rest.