Clothing
Why is clothing significant? Sure, people wear it to keep warm or to protect themselves from the elements. But if that were its sole purpose, why don't we all wear the same thing? Why are there so many different varieties of clothing?
Clothing reflects our identity. We wear who we are. From a business man's suit to a football fan's jersey, everything we wear is a reflection of how we see ourselves.
And the ability to clothe ourselves reflects that ability to define our identity. In jail, all inmates wear jumpsuits. Why? Through their choices, they've lost the ability to define their identity. It is now the jail that defines who they are, and that is reflected by their mandate of the jumpsuits.
So what does this have to do with Adam and Eve? Well, what is the first thing they do when their eyes are opened? "They sewed fig leaves together and made themselves aprons" (Moses 4:13). They made themselves clothing. And this clothing seems to say something about how they identified themselves in that moment. Although it may be that they used the fig leaves simply because they were big, so it didn't require a lot to make aprons, it is also very possible that fig leaves were used because they would provide good camouflage. Adam and Eve didn't feel worthy to be in God's presence anymore, so the best thing they felt they could to was hide, which they proceed to do.
God still seeks them out, however. He asks them why they were hiding, and each in turn takes responsibility for their choice to partake of the fruit. After explaining the consequences of their choices, God then makes them a gift. He makes them coats of skins, showing them something that they couldn't see on their own: God didn't want them to hide from Him. In clothing them, God exercised His powers to identify Adam and Eve, showing them that they didn't have to hide from God. God wanted to be a part of their identity. He wanted them to understand that one mistake didn't have to define them for the rest of eternity. They could form a society that involved God, that sought Him out often. He wanted His creation of society not to hide from Him, but to include Him.
At the end of the day, God wanted them back in His presence.