The author of this article goes into more depth on this deeply significant, simple story, and how God's decision to cast Adam and Eve out of the garden and subject them to physical death was a blessing, as allowing to immediately gain immortality would permanently trap them in a bad state. He continues:
Death in this sense is not the curse, but a gift from a gracious God who, having just made new garments for his frightened creation, understands that without limits placed upon their lives, being arum would be more intolerable than it already was. Imagine an eternity of toil and pain and estrangement described in verses 14-19. Thus, we see God already conceding to the theme. Adjusting to this new situation. There is already, in the beginning, a hint toward the second dominant theme of the biblical landscape — deliverance and restoration. But it originates in the open eyed acknowledgment of the fact of human arumness and the turbulence which follows that knowledge. This movement toward concession culminates in the covenant.
This fits is nicely with themes developed by Lehi in 2 Nephi 2, Jacob in 2 Nephi 9, and Alma in Alma 12/13 and Alma 42. The fall of Adam and Eve brings them knowledge but separates them from God (lest God's plan be frustrated), and mortality becomes a probationary time to choose to return to Him. The covenant God gives to Adam and Eve as he clothes them and send them away is to "cover their nakedness" (or perhaps in other words, compensate for their shrewdness) as they go about their mortal journey. In the words of this pastor:
The covenant — this rich mixture of tradition, experience, ritual, story and law makes it possible to live in community and is above all a gracious gesture toward human weakness. It proves itself time and again in the narrative of the biblical epic and in our own lives. Within its borders we come to trust, no longer fearing others discovering who we are, or needing to expend the enormous energy necessary for denial. The covenant concedes it!
When I sit in a pew next to you on Sunday morning I am transparent as Adam and so are you. The journey into Lent, the passion of Jesus, highlights this reality. In fact, we are sitting in the same pew because our eyes have been opened and we have grown weary of denying and displacing blame for our humanness. This covenant, flowing from the fullness of God's love, allows for us to be as it was 'in the beginning': now the two of them were arum, yet they were not ashamed, neither were they frightened.