BBC: Genesis 3:20-21
The man called his wife's name Eve, because she was the mother of all living. And the Lord God made for Adam and for his wife garments of skins and clothed them. - Genesis 3:20-21
This verse contains many subtle things. Eve's name in Hebrew (Chavvah) comes from the word for life (chay). This is the same word that is used even of the breathe of life found in the creation of Adam (Gen 2:7). In this one could argue that all subsequent life stems from Eve. Whether or not this includes the human soul is a theological debate left alone.
The importance in this text lies in the clothing of Adam and Eve. While minor attention is often spent on their nakedness, much attention is spent on clothing. The clothing of the naked couple is God's first step to restore the fellowship of the Creator and creation. What Adam and Eve attempted on their own failed (Gen 3:7). This was to show that works of the law would never bring back fellowship. Instead solely the grace of God is permissible.
The clothing of the first couple is fulfilled in the clothing of the church. Those who have learned Christ have put on Christ (Eph 4:21-23) and all baptized have put on Christ (Gal 3:27). This clothing of Christ is the beautiful fulfillment of God's desire to clothe His people. That Christ is the God-man and the only bridge between Creator and creation brings a joyful fulfillment to this passage.
*The Bible Blogging Commentary is a slow and simple treading of the Scriptures. No quotes from other theologians and no explicit Greek/Hebrew lessons.*