Quote from John Walton, The Lost World of Genesis One: Ancient Cosmology and the Origins Debate (pp. 146-7):
The fourth commandment directs people to observe the sabbath based on God's rest in Genesis 1. Throughout human history interpreters of Scripture have struggled to work out the implications of this directive. What constitutes rest? What activities are ruled out? Part of the difficulty is that the Bible offers little detail as it tends more toward vague generalizations. Furthermore most of the statements are negative (what one should not do) rather than positive (approved or even mandated activities).
Given the view of Genesis 1 presented in this book, we get a new way to think about the sabbath. if God's rest on the seventh day involved him taking up his presence in his cosmic temple which has been ordered and made functional so that he is now ready to run the cosmos, our sabbath rest can be seen in a different light. Obviously, God is not asking us to imitate his sabbath rest by taking the functional controls. I would suggest that instead he is asking us to recognize that he is at the controls, not us. When we "rest" on the sabbath, we recognize him as the author of order and the one who brings rest (stability) to our lives and world. We take our hands off the controls of our lives and acknowledge him as the one who is in control. Most importantly this calls on us to step back from our workaday world—those means by which we try to provide for ourselves and gain control of our circumstances. Sabbath is for recognizing that it is God who provides for us and who is the master of our lives and our world. We are not imitating him in sabbath observance, we are acknowledging him in tangible ways.
That doesn't say everything that could be said about the significance of the 4th commandment under the new covenant, but I think it's a fruitful way for Christians to think about keeping the sabbath day holy. I hope to write more about Walton's fascinating -- and paradigm altering -- view of Genesis 1, but now I'm going to take a Sunday afternoon nap!