God instructs us to rest in order for us to recognize that we are dependent upon Him. It is not our hard work and "pulling ourselves up by our bootstraps" which allows us to live, to eat, and to pay our bills. Every breath we take is given by God. Every morsel of food is provided by Him. When we rest from our labor as He instructed and trust in Him to provide, we free ourselves from the very American notion of self-reliance, which is a source of the increased stress so many of us are under.
God instructed the Israelites to rest on the seventh day and to allow the land to rest for an entire year in the seventh year. They were not to even gather in what the land produced on its own that year. God promised that He would provide enough in the sixth year to carry them through until the harvest from the eighth year. We now understand the scientific reasons why this was true - allowing the land to lie fallow enriches the soil and produces better crops. But even more than the scientific basis, there is a spiritual basis for this principle. Our food, our lives, do not come from the land, but from the Lord.
Trusting God to provide for us is liberating. It is not that we sit idle and expect God's provision, but if we are working and resting as God has instructed, we are freed from the worry of dependence on our own abilities. There is liberty in trusting God to provide.