Why did God make garments of skin for Adam and Eve when they had already made clothing for themselves? Immediately after Adam and Eve sinned, we are told that they made clothing for themselves.


  Then the eyes of both were opened, and they knew that they were naked. And they sewed fig leaves together and made themselves loincloths.  Genesis 3:7 ESV


However, after God comes into the garden, He also makes clothing for them.


  And the Lord God made for Adam and for his wife garments of skins and clothed them.  Genesis 3:21 ESV


Why does God do this when Adam and Eve were already clothed?  What was wrong with the clothing they already had, and what was right about the clothing that God made for them?
When Adam and Eve sinned in the garden, God gave them skins to cover up with (Genesis 3:21). To get those skins, some animal had to die. In other words, God sacrificed an animal to cover their sin1. From the beginning, God has declared the payment for sin is death, and so blood must be shed to cover sin:

Leviticus 17:11: “For the life of a creature is in the blood, and I have given it to you to make atonement for yourselves on the altar; it is the blood that makes atonement for one’s life.”
Hebrews 9:22: “In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness.”

Early in the Old Testament God introduced this idea of one innocent being shedding its blood in place of the sinner’s.
However the solution of sacrificing bulls and goats and lambs for the sins of each person’s sin was a temporary fix. The next year, another animal would have to be sacrificed for the same person. A more permanent solution was needed, as noted in Hebrews 10:4

For it is impossible for the blood of bulls and goats to take away sins.

That meant a human was needed to die for humans’ sin. But all humans are sinful, so another sin-filled person dying for us just wouldn’t work. A human without sin was needed.
But ever since Adam, every human born is sin-filled, so how could a sinless man happen? The only way was if God did it Himself.
God Himself became a man: Jesus means “the LORD saves” and died for us in our place. Therefore, anyone who accepts the sacrifice of Jesus on his or her behalf is covered by his blood and is saved.
1An explanation of the idea that God provided the skins by killing the first animals to powerfully show Adam and Eve the result of their sin, and the idea that this typified the death of Christ can be found in Matthew Henry's Commentary on the Holy Bible.